Notes Payable - Callable Medium-Term Notes (Details) - USD ($) $ in Thousands	Mar. 31, 2021	Dec. 31, 2020
Debt Instrument [Line Items]
2023	$ 2,912,497	$ 3,004,203
2024	2,509,857	2,809,551
2025	1,308,945	927,119
Total principal net of discounts	$ 21,536,571	$ 21,795,677
Weighted - average rate (as a percent)	1.25%	1.37%
2022
Debt Instrument [Line Items]
2022	$ 2,719,969
Weighted - average rate (as a percent)	1.06%
2023
Debt Instrument [Line Items]
2023	$ 2,479,427
Weighted - average rate (as a percent)	1.24%
2024
Debt Instrument [Line Items]
2024	$ 1,247,008
Weighted - average rate (as a percent)	1.28%
2025
Debt Instrument [Line Items]
2025	$ 1,283,087
Weighted - average rate (as a percent)	1.00%
Thereafter
Debt Instrument [Line Items]
Thereafter	$ 3,520,003
Weighted - average rate (as a percent)	1.82%
Call Option
Debt Instrument [Line Items]
2022	$ 350,449
2023	355,710
2024	119,413
2025	267,726
Thereafter	788,996
Total principal net of discounts	$ 1,882,294
Weighted - average rate (as a percent)	0.98%
Call Option \| 2022
Debt Instrument [Line Items]
Weighted - average rate (as a percent)	0.27%
Call Option \| 2023
Debt Instrument [Line Items]
Weighted - average rate (as a percent)	0.77%
Call Option \| 2024
Debt Instrument [Line Items]
Weighted - average rate (as a percent)	1.09%
Call Option \| 2025
Debt Instrument [Line Items]
Weighted - average rate (as a percent)	0.83%
Call Option \| Thereafter
Debt Instrument [Line Items]
Weighted - average rate (as a percent)	1.44%

Long-Term Debt, Maturity, after Year Four

No definition available.

Name:	agm_LongTermDebtMaturityAfterYearFour
Namespace Prefix:	agm_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount, after unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(3)
-URI http://asc.fasb.org/extlink&oid=120520924&loc=SL6031897-161870

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04.(a))
-URI http://asc.fasb.org/extlink&oid=120395691&loc=d3e24072-122690

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 10
-Section 50
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=6802200&loc=d3e1835-112601

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Weighted average interest rate of long-term debt outstanding calculated at point in time.

+ References

No definition available.

+ Details

Name:	us-gaap_LongtermDebtWeightedAverageInterestRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueYearOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueYearTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueYearThreeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueYearFourMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=agm_DueAfterFourYearsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=us-gaap_CallOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: