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LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of Loans Receivable, Net) (Details) (USD $)
In Thousands, unless otherwise specified
Dec. 31, 2014
Sep. 30, 2014
Accounts, Notes, Loans and Financing Receivable [Line Items]    
Loans and Leases Receivable, Gross $ 410,518us-gaap_LoansAndLeasesReceivableGrossCarryingAmount $ 406,813us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
Net deferred loan costs 194us-gaap_LoansAndLeasesReceivableDeferredIncome 217us-gaap_LoansAndLeasesReceivableDeferredIncome
Allowance for loan losses (2,939)us-gaap_LoansAndLeasesReceivableAllowance (2,835)us-gaap_LoansAndLeasesReceivableAllowance
Total loans receivable, net 407,773us-gaap_LoansAndLeasesReceivableNetReportedAmount 404,195us-gaap_LoansAndLeasesReceivableNetReportedAmount
One-to four-family residential    
Accounts, Notes, Loans and Financing Receivable [Line Items]    
Loans and Leases Receivable, Gross 159,988us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
160,335us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
Allowance for loan losses (474)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
(402)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
Commercial real estate    
Accounts, Notes, Loans and Financing Receivable [Line Items]    
Loans and Leases Receivable, Gross 170,347us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
169,449us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
Allowance for loan losses (832)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
(826)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
Construction    
Accounts, Notes, Loans and Financing Receivable [Line Items]    
Loans and Leases Receivable, Gross 12,782us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
12,232us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
Allowance for loan losses (748)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
(784)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
Home equity lines of credit    
Accounts, Notes, Loans and Financing Receivable [Line Items]    
Loans and Leases Receivable, Gross 21,056us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
19,366us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
Allowance for loan losses (66)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
(62)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
Commercial business    
Accounts, Notes, Loans and Financing Receivable [Line Items]    
Loans and Leases Receivable, Gross 36,254us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
35,035us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
Allowance for loan losses (733)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
(643)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
Other    
Accounts, Notes, Loans and Financing Receivable [Line Items]    
Loans and Leases Receivable, Gross 10,091us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
10,396us-gaap_LoansAndLeasesReceivableGrossCarryingAmount
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
Allowance for loan losses $ (6)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
$ (9)us-gaap_LoansAndLeasesReceivableAllowance
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember