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LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of Average Recorded Investment in Impaired Loans) (Details) (USD $) In Thousands, unless otherwise specified	3 Months Ended		6 Months Ended
	Mar. 31, 2015	Mar. 31, 2014	Mar. 31, 2015	Mar. 31, 2014
Financing Receivable, Impaired [Line Items]
Average investment in impaired loans	$ 16,477us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment	$ 23,293us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment	$ 16,724us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment	$ 23,964us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
One-to four-family residential [Member]
Financing Receivable, Impaired [Line Items]
Average investment in impaired loans	6,937us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember	13,610us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember	7,532us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember	13,963us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = mgyr_Residential1To4FamilyRealEstateMember
Commercial real estate
Financing Receivable, Impaired [Line Items]
Average investment in impaired loans	5,215us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember	5,206us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember	5,159us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember	5,477us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialRealEstateMember
Construction
Financing Receivable, Impaired [Line Items]
Average investment in impaired loans	1,942us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember	2,736us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember	2,054us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember	2,989us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_ConstructionLoansMember
Home equity lines of credit
Financing Receivable, Impaired [Line Items]
Average investment in impaired loans	484us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember	1,135us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember	599us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember	1,099us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_HomeEquityMember
Commercial business
Financing Receivable, Impaired [Line Items]
Average investment in impaired loans	$ 1,899us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember	$ 607us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember	$ 1,380us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember	$ 436us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment / us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis = us-gaap_CommercialLoanMember

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Average amount of investment of impaired financing receivables with related allowance for credit losses and without a related allowance for credit losses.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 310

-SubTopic 10

-Section 50

-Paragraph 15

-Subparagraph (c)(1)

-URI http://asc.fasb.org/extlink&oid=35738203&loc=d3e5212-111524



Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 310

-SubTopic 10

-Section 50

-Paragraph 17

-URI http://asc.fasb.org/extlink&oid=35738203&loc=d3e5258-111524

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