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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
Dec. 31, 2014
Dec. 31, 2013
Financing Receivable, Impaired [Line Items]    
Average investment in impaired loans $ 17,277us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment $ 24,126us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
One-to four-family residential [Member]    
Financing Receivable, Impaired [Line Items]    
Average investment in impaired loans 8,401us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
14,257us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
Commercial real estate    
Financing Receivable, Impaired [Line Items]    
Average investment in impaired loans 4,980us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
5,560us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
Construction    
Financing Receivable, Impaired [Line Items]    
Average investment in impaired loans 2,231us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
3,196us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
Home equity lines of credit    
Financing Receivable, Impaired [Line Items]    
Average investment in impaired loans 479us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
1,027us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
Commercial business    
Financing Receivable, Impaired [Line Items]    
Average investment in impaired loans $ 1,187us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
$ 88us-gaap_ImpairedFinancingReceivableAverageRecordedInvestment
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember