Note 3 - Investment Securities - Investments in Debt Securities (Details) - USD ($)	Mar. 31, 2022	Dec. 31, 2021
Amortized cost, available for sale	$ 156,561,411	$ 151,162,429
Unrealized gains, available for sale	45,320	412,772
Unrealized losses, available for sale	10,890,296	2,337,285
Fair value, available for sale	145,716,435	149,237,916
Amortized cost, held to maturity	21,343,559	21,851,975
Fair value, held to maturity	20,914,769
US States and Political Subdivisions Debt Securities [Member]
Amortized cost, available for sale	752,413	753,061
Unrealized gains, available for sale	730	10,437
Unrealized losses, available for sale	5,780	0
Fair value, available for sale	747,363	763,498
Amortized cost, held to maturity	21,343,559	21,851,975
Unrealized gains, held to maturity	156,037	1,020,877
Unrealized losses, held to maturity	584,827	67,251
Fair value, held to maturity	20,914,769	22,805,601
SBA Pools [Member]
Amortized cost, available for sale	1,300,202	1,418,770
Unrealized gains, available for sale	1,682	1,656
Unrealized losses, available for sale	22,049	22,664
Fair value, available for sale	1,279,835	1,397,762
Corporate Debt Securities [Member]
Amortized cost, available for sale	10,960,028	9,225,153
Unrealized gains, available for sale	15,803	64,595
Unrealized losses, available for sale	347,754	55,541
Fair value, available for sale	10,628,077	9,234,207
Collateralized Mortgage-Backed Securities [Member]
Amortized cost, available for sale	143,548,768	139,765,445
Unrealized gains, available for sale	27,105	336,084
Unrealized losses, available for sale	10,514,713	2,259,080
Fair value, available for sale	$ 133,061,160	$ 137,842,449

Amount, before tax, of unrealized gain in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

+ Details

Name:	us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, before tax, of unrealized loss in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

+ Details

Name:	us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amortized cost of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124258926&loc=SL82898722-210454

+ Details

Name:	us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(6))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124258926&loc=SL82898722-210454

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=124260329&loc=d3e26610-111562

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (aa)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

+ Details

Name:	us-gaap_AvailableForSaleSecuritiesDebtSecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount, before allowance for credit loss, of investment in debt security measured at amortized cost (held-to-maturity).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124255206&loc=SL82895884-210446

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 14
-URI https://asc.fasb.org/extlink&oid=124255953&loc=SL82919253-210447

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 7A
-URI https://asc.fasb.org/extlink&oid=123577603&loc=SL6953401-111524

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 5
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27232-111563

+ Details

Name:	us-gaap_HeldToMaturitySecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of accumulated unrecognized gain on investment in debt security measured at amortized cost (held-to-maturity).

+ References

+ Details

Name:	us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of accumulated unrealized loss on investment in debt security measured at amortized cost (held-to-maturity).

+ References

+ Details

Name:	us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Fair value of investment in debt security measured at amortized cost (held-to-maturity).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 5
-Subparagraph (aa)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27232-111563

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(6))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 5A
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=SL120269820-111563

+ Details

Name:	us-gaap_HeldToMaturitySecuritiesFairValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_USStatesAndPoliticalSubdivisionsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=fmfg_SBAPoolsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_CorporateDebtSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_MortgageBackedSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: