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Subsequent Event (Details) - CoBank, ACB [Member] - Common Class B [Member] - USD ($) $ in Millions | Feb. 19, 2019 | Dec. 31, 2018
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Subsequent Event [Line Items] |  |
Common Stock Ownership Percentage by a Related Party |  | 32.60%
Subsequent Event [Member] |  |
Subsequent Event [Line Items] |  |
Related Party Transaction, Purchases from Related Party | $ 546.0 |

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- Definition Common Stock Ownership Percentage by a Related Party + References No definition available. + Details
Name: | agm_CommonStockOwnershipPercentageByRelatedParty
Namespace Prefix: | agm_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | instant

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- Definition Purchases during the period (excluding transactions that are eliminated in consolidated or combined financial statements) with related party. + References No definition available. + Details
Name: | us-gaap_RelatedPartyTransactionPurchasesFromRelatedParty
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Detail information of subsequent event by type. User is expected to use existing line items from elsewhere in the taxonomy as the primary line items for this disclosure, which is further associated with dimension and member elements pertaining to a subsequent event. + References No definition available. + Details
Name: | us-gaap_SubsequentEventLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Details
Name: | us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=agm_CobankAcbMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassBMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |