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BORROWINGS (Schedule of Short-Term Arrangements With the FHLBNY) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2019 | Sep. 30, 2018
Debt Disclosure [Abstract] |  |
Balance at end of year |  |
Weighted average balance during the year | 743 | 3,418
Maximum month-end balance during the year | $ 16,800 | $ 25,175
Average interest rate during the year | 2.45% | 2.16%

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- Definition Short term Federal Home Loan Bank borrowings of the latest balance sheet date. + References No definition available. + Details
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Namespace Prefix: | mgyr_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- References No definition available. + Details
Name: | us-gaap_DebtDisclosureAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition The calculated average balance outstanding for the year for all Federal Home Loan Bank advances as of the Balance Sheet date. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 942 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.9-03.13(3)(a)) -URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878 + Details
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Balance Type: | credit
Period Type: | duration

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- Definition The calculated weighted average interest rate for Federal Home Loan Bank advances for the period ended as of the Balance Sheet date. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 942 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.9-03.13(3)(a)) -URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878 + Details
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Balance Type: | na
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- Definition The maximum balance outstanding at any month end during the period as of the Balance Sheet date. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 942 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.9-03.13(3)(a)) -URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878 + Details
Name: | us-gaap_FederalHomeLoanBankAdvancesActivityForYearMaximumOutstandingAtAnyMonthEnd
Namespace Prefix: | us-gaap_
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Balance Type: | credit
Period Type: | instant