<?xml version="1.0" encoding="US-ASCII" standalone="no"?>
<!--Generated by ThunderDome XBRL - 02:20PM UTC 2026-03-26--><link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-consolidated-balance-sheets" xlink:href="fmfg-20251231.xsd#statement-consolidated-balance-sheets" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-consolidated-balance-sheets" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital" xlink:label="us-gaap_AdditionalPaidInCapital" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdvancesFromFederalHomeLoanBanks" xlink:label="us-gaap_AdvancesFromFederalHomeLoanBanks" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BankOwnedLifeInsurance" xlink:label="us-gaap_BankOwnedLifeInsurance" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndDueFromBanks" xlink:label="us-gaap_CashAndDueFromBanks" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsAndFederalFundsSold" xlink:label="us-gaap_CashCashEquivalentsAndFederalFundsSold" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxAssetsNet" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Deposits" xlink:label="us-gaap_Deposits" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNi" xlink:label="us-gaap_EquitySecuritiesFvNi" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalHomeLoanBankStock" xlink:label="us-gaap_FederalHomeLoanBankStock" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:label="us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:label="us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestBearingDepositLiabilities" xlink:label="us-gaap_InterestBearingDepositLiabilities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestBearingDepositsInBanks" xlink:label="us-gaap_InterestBearingDepositsInBanks" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPayableCurrentAndNoncurrent" xlink:label="us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestReceivable" xlink:label="us-gaap_InterestReceivable" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt" xlink:label="us-gaap_LongTermDebt" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageLoansOnRealEstate" xlink:label="us-gaap_MortgageLoansOnRealEstate" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestBearingDepositLiabilities" xlink:label="us-gaap_NoninterestBearingDepositLiabilities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssets" xlink:label="us-gaap_OtherAssets" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilities" xlink:label="us-gaap_OtherLiabilities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherRealEstate" xlink:label="us-gaap_OtherRealEstate" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:label="us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositsAtCarryingValue" xlink:label="us-gaap_TimeDepositsAtCarryingValue" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsAndFederalFundsSold" xlink:to="us-gaap_CashAndDueFromBanks" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsAndFederalFundsSold" xlink:to="us-gaap_InterestBearingDepositsInBanks" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_EquitySecuritiesFvNi" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_FederalHomeLoanBankStock" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_MortgageLoansOnRealEstate" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_InterestReceivable" xlink:type="arc"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_DeferredIncomeTaxAssetsNet" xlink:type="arc"/>
    <link:calculationArc order="9" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_OtherRealEstate" xlink:type="arc"/>
    <link:calculationArc order="10" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_BankOwnedLifeInsurance" xlink:type="arc"/>
    <link:calculationArc order="11" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:type="arc"/>
    <link:calculationArc order="12" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_OtherAssets" xlink:type="arc"/>
    <link:calculationArc order="13" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_CashCashEquivalentsAndFederalFundsSold" xlink:type="arc"/>
    <link:calculationArc order="14" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_TimeDepositsAtCarryingValue" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_NoninterestBearingDepositLiabilities" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_InterestBearingDepositLiabilities" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_OtherLiabilities" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Deposits" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_AdvancesFromFederalHomeLoanBanks" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_LongTermDebt" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_CommonStockValue" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_AdditionalPaidInCapital" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_Liabilities" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_StockholdersEquity" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-consolidated-statements-of-income-" xlink:href="fmfg-20251231.xsd#statement-consolidated-statements-of-income-" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-consolidated-statements-of-income-" xlink:type="extended">
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_AutomatedTellerMachineAndDebitCardExpense" xlink:label="fmfg_AutomatedTellerMachineAndDebitCardExpense" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_InterestIncomeFromFederalFundssOldAndOtherInterestEarningAssets" xlink:label="fmfg_InterestIncomeFromFederalFundssOldAndOtherInterestEarningAssets" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_OtherRealEstateOwnedNet" xlink:label="fmfg_OtherRealEstateOwnedNet" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_PostageDeliveryAndArmoredCarrierExpense" xlink:label="fmfg_PostageDeliveryAndArmoredCarrierExpense" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdvertisingExpense" xlink:label="us-gaap_AdvertisingExpense" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BankOwnedLifeInsuranceIncome" xlink:label="us-gaap_BankOwnedLifeInsuranceIncome" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:label="us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeBenefitsAndShareBasedCompensation" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensation" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquipmentExpense" xlink:label="us-gaap_EquipmentExpense" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:label="us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:label="us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:label="us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossFromHedgedFirmCommitmentNotQualifyingAsFairValueHedgeNet" xlink:label="us-gaap_GainLossFromHedgedFirmCommitmentNotQualifyingAsFairValueHedgeNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSalesOfLoansNet" xlink:label="us-gaap_GainLossOnSalesOfLoansNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainOnBusinessInterruptionInsuranceRecovery" xlink:label="us-gaap_GainOnBusinessInterruptionInsuranceRecovery" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeOperating" xlink:label="us-gaap_InterestAndDividendIncomeOperating" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:label="us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDeposits" xlink:label="us-gaap_InterestExpenseDeposits" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseFederalHomeLoanBankAndFederalReserveBankAdvancesLongTerm" xlink:label="us-gaap_InterestExpenseFederalHomeLoanBankAndFederalReserveBankAdvancesLongTerm" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseLoansFromOtherFederalHomeLoanBanks" xlink:label="us-gaap_InterestExpenseLoansFromOtherFederalHomeLoanBanks" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseOperating" xlink:label="us-gaap_InterestExpenseOperating" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseOtherLongTermDebt" xlink:label="us-gaap_InterestExpenseOtherLongTermDebt" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseSecuritiesSoldUnderAgreementsToRepurchase" xlink:label="us-gaap_InterestExpenseSecuritiesSoldUnderAgreementsToRepurchase" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:label="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeExpenseNet" xlink:label="us-gaap_InterestIncomeExpenseNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeSecuritiesTaxExempt" xlink:label="us-gaap_InterestIncomeSecuritiesTaxExempt" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeSecuritiesTaxable" xlink:label="us-gaap_InterestIncomeSecuritiesTaxable" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LaborAndRelatedExpense" xlink:label="us-gaap_LaborAndRelatedExpense" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestExpense" xlink:label="us-gaap_NoninterestExpense" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestIncome" xlink:label="us-gaap_NoninterestIncome" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OccupancyNet" xlink:label="us-gaap_OccupancyNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNoninterestExpense" xlink:label="us-gaap_OtherNoninterestExpense" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfessionalFees" xlink:label="us-gaap_ProfessionalFees" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForLoanLossesExpensed" xlink:label="us-gaap_ProvisionForLoanLossesExpensed" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestAndDividendIncomeOperating" xlink:to="us-gaap_InterestIncomeSecuritiesTaxExempt" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestAndDividendIncomeOperating" xlink:to="fmfg_InterestIncomeFromFederalFundssOldAndOtherInterestEarningAssets" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestAndDividendIncomeOperating" xlink:to="us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestAndDividendIncomeOperating" xlink:to="us-gaap_InterestIncomeSecuritiesTaxable" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestExpenseOperating" xlink:to="us-gaap_InterestExpenseOtherLongTermDebt" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestExpenseOperating" xlink:to="us-gaap_InterestExpenseDeposits" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestExpenseOperating" xlink:to="us-gaap_InterestExpenseSecuritiesSoldUnderAgreementsToRepurchase" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestExpenseOperating" xlink:to="us-gaap_InterestExpenseLoansFromOtherFederalHomeLoanBanks" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestExpenseOperating" xlink:to="us-gaap_InterestExpenseFederalHomeLoanBankAndFederalReserveBankAdvancesLongTerm" xlink:type="arc"/>
    <link:calculationArc order="0" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestIncomeExpenseNet" xlink:to="us-gaap_InterestExpenseOperating" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestIncomeExpenseNet" xlink:to="us-gaap_InterestAndDividendIncomeOperating" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:to="us-gaap_InterestIncomeExpenseNet" xlink:type="arc"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:to="us-gaap_ProvisionForLoanLossesExpensed" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_DebtAndEquitySecuritiesRealizedGainLoss" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_GainLossFromHedgedFirmCommitmentNotQualifyingAsFairValueHedgeNet" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_GainLossOnSalesOfLoansNet" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_GainOnBusinessInterruptionInsuranceRecovery" xlink:type="arc"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:type="arc"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:type="arc"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_BankOwnedLifeInsuranceIncome" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="fmfg_PostageDeliveryAndArmoredCarrierExpense" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_AdvertisingExpense" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_LaborAndRelatedExpense" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="fmfg_OtherRealEstateOwnedNet" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_EmployeeBenefitsAndShareBasedCompensation" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_OtherNoninterestExpense" xlink:type="arc"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_OccupancyNet" xlink:type="arc"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_EquipmentExpense" xlink:type="arc"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_ProfessionalFees" xlink:type="arc"/>
    <link:calculationArc order="9" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="fmfg_AutomatedTellerMachineAndDebitCardExpense" xlink:type="arc"/>
    <link:calculationArc order="10" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:type="arc"/>
    <link:calculationArc order="0" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_NoninterestExpense" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_NoninterestIncome" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-consolidated-statements-of-comprehensive-income-" xlink:href="fmfg-20251231.xsd#statement-consolidated-statements-of-comprehensive-income-" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-consolidated-statements-of-comprehensive-income-" xlink:type="extended">
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesRealizedLosses" xlink:label="fmfg_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesRealizedLosses" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:label="us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesTax" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:type="arc"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="fmfg_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesRealizedLosses" xlink:type="arc"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesTax" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeAvailableforsaleSecuritiesAdjustmentNetOfTaxPortionAttributableToParent" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_NetIncomeLoss" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-consolidated-statements-of-cash-flows-" xlink:href="fmfg-20251231.xsd#statement-consolidated-statements-of-cash-flows-" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-consolidated-statements-of-cash-flows-" xlink:type="extended">
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_AmortizationOfDebtIssuanceCostsNet" xlink:label="fmfg_AmortizationOfDebtIssuanceCostsNet" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_IncreaseDecreaseInBankOwnedLifeInsuranceCashSurrenderValue" xlink:label="fmfg_IncreaseDecreaseInBankOwnedLifeInsuranceCashSurrenderValue" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_IncreaseDecreaseInMortgageLoansHeldforsaleExcludingCollectionOfMortgageLoansHeldforsale" xlink:label="fmfg_IncreaseDecreaseInMortgageLoansHeldforsaleExcludingCollectionOfMortgageLoansHeldforsale" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_LongtermDebtPrincipalPaymentNet" xlink:label="fmfg_LongtermDebtPrincipalPaymentNet" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_NoncashCompensation" xlink:label="fmfg_NoncashCompensation" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_PaymentsForBankOwnedLifeInsurance" xlink:label="fmfg_PaymentsForBankOwnedLifeInsurance" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_PaymentsForEquitySecuritiesDividendReinvested" xlink:label="fmfg_PaymentsForEquitySecuritiesDividendReinvested" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_PaymentsForProceedsFromLoansMadeToCustomersNetOfPrincipalCollected" xlink:label="fmfg_PaymentsForProceedsFromLoansMadeToCustomersNetOfPrincipalCollected" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_ProceedsFromFederalReserveBankAdvances" xlink:label="fmfg_ProceedsFromFederalReserveBankAdvances" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_ProceedsFromPaymentsForFederalHomeLoanBankAdvances" xlink:label="fmfg_ProceedsFromPaymentsForFederalHomeLoanBankAdvances" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_RightofuseAssetAmortization" xlink:label="fmfg_RightofuseAssetAmortization" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_WriteDownOfOtherRealEstateOwned" xlink:label="fmfg_WriteDownOfOtherRealEstateOwned" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleGainLoss" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleGainLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationAmortizationAndAccretionNet" xlink:label="us-gaap_DepreciationAmortizationAndAccretionNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeGainLossOnDerivativeNet" xlink:label="us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:label="us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossFromHedgedFirmCommitmentNotQualifyingAsFairValueHedgeNet" xlink:label="us-gaap_GainLossFromHedgedFirmCommitmentNotQualifyingAsFairValueHedgeNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnDispositionOfAssets" xlink:label="us-gaap_GainLossOnDispositionOfAssets" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSalesOfLoansNet" xlink:label="us-gaap_GainLossOnSalesOfLoansNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainOnBusinessInterruptionInsuranceRecovery" xlink:label="us-gaap_GainOnBusinessInterruptionInsuranceRecovery" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:label="us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:label="us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherDeferredLiability" xlink:label="us-gaap_IncreaseDecreaseInOtherDeferredLiability" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetChangeInterestBearingDepositsDomestic" xlink:label="us-gaap_NetChangeInterestBearingDepositsDomestic" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetChangeNoninterestBearingDepositsDomestic" xlink:label="us-gaap_NetChangeNoninterestBearingDepositsDomestic" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromFederalHomeLoanBankStock" xlink:label="us-gaap_PaymentsForProceedsFromFederalHomeLoanBankStock" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividends" xlink:label="us-gaap_PaymentsOfDividends" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireHeldToMaturitySecurities" xlink:label="us-gaap_PaymentsToAcquireHeldToMaturitySecurities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireProductiveAssets" xlink:label="us-gaap_PaymentsToAcquireProductiveAssets" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:label="us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfSubordinatedLongTermDebt" xlink:label="us-gaap_ProceedsFromIssuanceOfSubordinatedLongTermDebt" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:label="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfHeldToMaturitySecurities" xlink:label="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfHeldToMaturitySecurities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase" xlink:label="us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:label="us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:label="us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForLoanLossesExpensed" xlink:label="us-gaap_ProvisionForLoanLossesExpensed" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation" xlink:label="us-gaap_ShareBasedCompensation" xlink:type="locator"/>
    <link:calculationArc order="0" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="fmfg_IncreaseDecreaseInBankOwnedLifeInsuranceCashSurrenderValue" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_DepreciationAmortizationAndAccretionNet" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInOtherDeferredLiability" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_ProvisionForLoanLossesExpensed" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="fmfg_RightofuseAssetAmortization" xlink:type="arc"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:type="arc"/>
    <link:calculationArc order="7" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:type="arc"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="fmfg_WriteDownOfOtherRealEstateOwned" xlink:type="arc"/>
    <link:calculationArc order="9" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="fmfg_IncreaseDecreaseInMortgageLoansHeldforsaleExcludingCollectionOfMortgageLoansHeldforsale" xlink:type="arc"/>
    <link:calculationArc order="10" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="fmfg_NoncashCompensation" xlink:type="arc"/>
    <link:calculationArc order="11" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:type="arc"/>
    <link:calculationArc order="12" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_GainLossOnDispositionOfAssets" xlink:type="arc"/>
    <link:calculationArc order="13" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc"/>
    <link:calculationArc order="14" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_GainLossOnSalesOfLoansNet" xlink:type="arc"/>
    <link:calculationArc order="15" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_GainOnBusinessInterruptionInsuranceRecovery" xlink:type="arc"/>
    <link:calculationArc order="16" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc"/>
    <link:calculationArc order="17" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_GainLossFromHedgedFirmCommitmentNotQualifyingAsFairValueHedgeNet" xlink:type="arc"/>
    <link:calculationArc order="18" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc"/>
    <link:calculationArc order="19" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleGainLoss" xlink:type="arc"/>
    <link:calculationArc order="20" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_ShareBasedCompensation" xlink:type="arc"/>
    <link:calculationArc order="21" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="fmfg_AmortizationOfDebtIssuanceCostsNet" xlink:type="arc"/>
    <link:calculationArc order="22" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetIncomeLoss" xlink:type="arc"/>
    <link:calculationArc order="23" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="arc"/>
    <link:calculationArc order="0" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsForProceedsFromFederalHomeLoanBankStock" xlink:type="arc"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="fmfg_PaymentsForEquitySecuritiesDividendReinvested" xlink:type="arc"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="fmfg_PaymentsForBankOwnedLifeInsurance" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfHeldToMaturitySecurities" xlink:type="arc"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromInsuranceSettlementInvestingActivities" xlink:type="arc"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:type="arc"/>
    <link:calculationArc order="8" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquireProductiveAssets" xlink:type="arc"/>
    <link:calculationArc order="9" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:type="arc"/>
    <link:calculationArc order="10" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquireHeldToMaturitySecurities" xlink:type="arc"/>
    <link:calculationArc order="11" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="fmfg_PaymentsForProceedsFromLoansMadeToCustomersNetOfPrincipalCollected" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetChangeNoninterestBearingDepositsDomestic" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetChangeInterestBearingDepositsDomestic" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="fmfg_ProceedsFromPaymentsForFederalHomeLoanBankAdvances" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="fmfg_ProceedsFromFederalReserveBankAdvances" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_ProceedsFromIssuanceOfSubordinatedLongTermDebt" xlink:type="arc"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="fmfg_LongtermDebtPrincipalPaymentNet" xlink:type="arc"/>
    <link:calculationArc order="7" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_PaymentsOfDividends" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-1-summary-of-significant-accounting-policies-basic-and-diluted-earnings-per-share-details" xlink:href="fmfg-20251231.xsd#statement-note-1-summary-of-significant-accounting-policies-basic-and-diluted-earnings-per-share-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-1-summary-of-significant-accounting-policies-basic-and-diluted-earnings-per-share-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:label="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-3-investment-securities-contractual-maturities-details" xlink:href="fmfg-20251231.xsd#statement-note-3-investment-securities-contractual-maturities-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-3-investment-securities-contractual-maturities-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesRollingYearTwoThroughFiveAmortizedCostBasis" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesRollingYearTwoThroughFiveAmortizedCostBasis" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfter10Years" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfter10Years" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfter5Through10Years" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfter5Through10Years" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfterOneThroughFiveYears" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfterOneThroughFiveYears" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingWithinOneYear" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingWithinOneYear" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityWithoutSingleMaturityDate" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityWithoutSingleMaturityDate" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesFairValue" xlink:label="us-gaap_HeldToMaturitySecuritiesFairValue" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesRollingYearTwoThroughFiveAmortizedCostBasis" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfter10Years" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingWithinOneYear" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfterOneThroughFiveYears" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDateRollingAfter5Through10Years" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityAllocatedAndSingleMaturityDate" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLossMaturityWithoutSingleMaturityDate" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-5-loans-and-allowance-for-credit-losses-major-categories-of-loans-details" xlink:href="fmfg-20251231.xsd#statement-note-5-loans-and-allowance-for-credit-losses-major-categories-of-loans-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-5-loans-and-allowance-for-credit-losses-major-categories-of-loans-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableDeferredIncome" xlink:label="us-gaap_FinancingReceivableDeferredIncome" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:label="us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:label="us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:type="arc"/>
    <link:calculationArc order="2" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="us-gaap_FinancingReceivableDeferredIncome" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-6-premises-and-equipment-premises-and-equipment-details" xlink:href="fmfg-20251231.xsd#statement-note-6-premises-and-equipment-premises-and-equipment-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-6-premises-and-equipment-premises-and-equipment-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentGross" xlink:label="us-gaap_PropertyPlantAndEquipmentGross" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentNet" xlink:label="us-gaap_PropertyPlantAndEquipmentNet" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentGross" xlink:type="arc"/>
    <link:calculationArc order="1" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-8-commitments-and-contingencies-operating-lease-liabilities-details" xlink:href="fmfg-20251231.xsd#statement-note-8-commitments-and-contingencies-operating-lease-liabilities-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-8-commitments-and-contingencies-operating-lease-liabilities-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-9-interestbearing-deposits-classification-of-interestbearing-deposits-details" xlink:href="fmfg-20251231.xsd#statement-note-9-interestbearing-deposits-classification-of-interestbearing-deposits-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-9-interestbearing-deposits-classification-of-interestbearing-deposits-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositsMoneyMarketDeposits" xlink:label="us-gaap_DepositsMoneyMarketDeposits" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositsNegotiableOrderOfWithdrawalNOW" xlink:label="us-gaap_DepositsNegotiableOrderOfWithdrawalNOW" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepositsSavingsDeposits" xlink:label="us-gaap_DepositsSavingsDeposits" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestBearingDepositLiabilities" xlink:label="us-gaap_InterestBearingDepositLiabilities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestBearingDomesticDepositOtherTimeDeposit" xlink:label="us-gaap_InterestBearingDomesticDepositOtherTimeDeposit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit" xlink:label="us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestBearingDepositLiabilities" xlink:to="us-gaap_DepositsSavingsDeposits" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestBearingDepositLiabilities" xlink:to="us-gaap_TimeDepositsAtOrAboveFDICInsuranceLimit" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestBearingDepositLiabilities" xlink:to="us-gaap_InterestBearingDomesticDepositOtherTimeDeposit" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestBearingDepositLiabilities" xlink:to="us-gaap_DepositsNegotiableOrderOfWithdrawalNOW" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestBearingDepositLiabilities" xlink:to="us-gaap_DepositsMoneyMarketDeposits" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-9-interestbearing-deposits-certificates-of-deposit-maturity-schedule-details" xlink:href="fmfg-20251231.xsd#statement-note-9-interestbearing-deposits-certificates-of-deposit-maturity-schedule-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-9-interestbearing-deposits-certificates-of-deposit-maturity-schedule-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesYearFive" xlink:label="us-gaap_TimeDepositMaturitiesYearFive" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesYearFour" xlink:label="us-gaap_TimeDepositMaturitiesYearFour" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesYearOne" xlink:label="us-gaap_TimeDepositMaturitiesYearOne" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesYearThree" xlink:label="us-gaap_TimeDepositMaturitiesYearThree" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDepositMaturitiesYearTwo" xlink:label="us-gaap_TimeDepositMaturitiesYearTwo" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TimeDeposits" xlink:label="us-gaap_TimeDeposits" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearOne" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearTwo" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearThree" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearFour" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearFive" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-components-of-income-tax-expense-details" xlink:href="fmfg-20251231.xsd#statement-note-11-income-taxes-components-of-income-tax-expense-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-components-of-income-tax-expense-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentFederalTaxExpenseBenefit" xlink:label="us-gaap_CurrentFederalTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:label="us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:label="us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFederalStateAndLocalTaxExpenseBenefit" xlink:label="us-gaap_DeferredFederalStateAndLocalTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:label="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="us-gaap_CurrentFederalTaxExpenseBenefit" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredFederalStateAndLocalTaxExpenseBenefit" xlink:to="us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredFederalStateAndLocalTaxExpenseBenefit" xlink:to="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_DeferredFederalStateAndLocalTaxExpenseBenefit" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-reconciliation-of-effective-income-tax-rate-details" xlink:href="fmfg-20251231.xsd#statement-note-11-income-taxes-reconciliation-of-effective-income-tax-rate-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-reconciliation-of-effective-income-tax-rate-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseLifeInsurance" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseLifeInsurance" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseLifeInsurance" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseLifeInsurance" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationNondeductibleExpenseLifeInsurance" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseLifeInsurance" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-schedule-of-pretax-income-details" xlink:href="fmfg-20251231.xsd#statement-note-11-income-taxes-schedule-of-pretax-income-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-schedule-of-pretax-income-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-schedule-of-income-taxes-paid-details" xlink:href="fmfg-20251231.xsd#statement-note-11-income-taxes-schedule-of-income-taxes-paid-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-schedule-of-income-taxes-paid-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:label="us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:label="us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet" xlink:label="us-gaap_IncomeTaxesPaidNet" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxesPaidNet" xlink:to="us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxesPaidNet" xlink:to="us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-components-of-deferred-tax-expense-details" xlink:href="fmfg-20251231.xsd#statement-note-11-income-taxes-components-of-deferred-tax-expense-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-11-income-taxes-components-of-deferred-tax-expense-details" xlink:type="extended">
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_DeferredTaxAssetTaxDeferredExpenseReserveAndAccrualHeldToMaturitySecuritiesAllowanceForCreditLoss" xlink:label="fmfg_DeferredTaxAssetTaxDeferredExpenseReserveAndAccrualHeldToMaturitySecuritiesAllowanceForCreditLoss" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_DeferredTaxAssetTaxDeferredExpenseReserveAndAccrualUnfundedCommitmentsAllowanceForCreditLoss" xlink:label="fmfg_DeferredTaxAssetTaxDeferredExpenseReserveAndAccrualUnfundedCommitmentsAllowanceForCreditLoss" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_DeferredTaxAssetsLeaseLiabilityNetOfRightOfUseAsset" xlink:label="fmfg_DeferredTaxAssetsLeaseLiabilityNetOfRightOfUseAsset" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_DeferredTaxAssetsLiabilitiesDerivativeInstruments" xlink:label="fmfg_DeferredTaxAssetsLiabilitiesDerivativeInstruments" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_DeferredTaxAssetsNonaccrualInterest" xlink:label="fmfg_DeferredTaxAssetsNonaccrualInterest" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_DeferredTaxAssetsOtherRealEstateOwnedAllowanceForLoss" xlink:label="fmfg_DeferredTaxAssetsOtherRealEstateOwnedAllowanceForLoss" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_DeferredTaxLiabilitiesInsuranceProceedsFromStormDamage" xlink:label="fmfg_DeferredTaxLiabilitiesInsuranceProceedsFromStormDamage" xlink:type="locator"/>
    <link:loc xlink:href="fmfg-20251231.xsd#fmfg_DeferredTaxLiabilitiesPurchaseAccountingAdjustments" xlink:label="fmfg_DeferredTaxLiabilitiesPurchaseAccountingAdjustments" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsNet" xlink:label="us-gaap_DeferredTaxAssetsNet" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOther" xlink:label="us-gaap_DeferredTaxAssetsOther" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsPostretirementBenefits" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsPostretirementBenefits" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:label="us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilities" xlink:label="us-gaap_DeferredTaxLiabilities" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:label="us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:label="us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesOther" xlink:label="us-gaap_DeferredTaxLiabilitiesOther" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:label="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="fmfg_DeferredTaxAssetsLeaseLiabilityNetOfRightOfUseAsset" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="us-gaap_DeferredTaxAssetsOther" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="fmfg_DeferredTaxAssetTaxDeferredExpenseReserveAndAccrualHeldToMaturitySecuritiesAllowanceForCreditLoss" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="fmfg_DeferredTaxAssetTaxDeferredExpenseReserveAndAccrualUnfundedCommitmentsAllowanceForCreditLoss" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="fmfg_DeferredTaxAssetsOtherRealEstateOwnedAllowanceForLoss" xlink:type="arc"/>
    <link:calculationArc order="6" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="fmfg_DeferredTaxAssetsLiabilitiesDerivativeInstruments" xlink:type="arc"/>
    <link:calculationArc order="7" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="fmfg_DeferredTaxAssetsNonaccrualInterest" xlink:type="arc"/>
    <link:calculationArc order="8" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsPostretirementBenefits" xlink:type="arc"/>
    <link:calculationArc order="9" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsNet" xlink:to="us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:type="arc"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilitiesOther" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="fmfg_DeferredTaxLiabilitiesPurchaseAccountingAdjustments" xlink:type="arc"/>
    <link:calculationArc order="2" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:type="arc"/>
    <link:calculationArc order="3" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:type="arc"/>
    <link:calculationArc order="4" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:type="arc"/>
    <link:calculationArc order="5" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxLiabilities" xlink:to="fmfg_DeferredTaxLiabilitiesInsuranceProceedsFromStormDamage" xlink:type="arc"/>
    <link:calculationArc order="0" weight="-1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="us-gaap_DeferredTaxLiabilities" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="us-gaap_DeferredTaxAssetsNet" xlink:type="arc"/>
  </link:calculationLink>
  <link:roleRef roleURI="http://www.fmb.com/20251231/role/statement-note-13-derivative-financial-instruments-derivative-instruments-gain-loss-details" xlink:href="fmfg-20251231.xsd#statement-note-13-derivative-financial-instruments-derivative-instruments-gain-loss-details" xlink:type="simple"/>
  <link:calculationLink xlink:role="http://www.fmb.com/20251231/role/statement-note-13-derivative-financial-instruments-derivative-instruments-gain-loss-details" xlink:type="extended">
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:label="us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:label="us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:type="locator"/>
    <link:loc xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:label="us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:type="locator"/>
    <link:calculationArc order="0" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:to="us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:type="arc"/>
    <link:calculationArc order="1" weight="1.0" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueHedgeIncludedInEffectivenessGainLoss" xlink:to="us-gaap_ChangeInUnrealizedGainLossOnHedgedItemInFairValueHedge1" xlink:type="arc"/>
  </link:calculationLink>
</link:linkbase>
