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LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of Activity in the Allowance for Loan Losses by Loan Category) (Details) (USD $)
In Thousands, unless otherwise specified
3 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Activity in the allowance for loan losses by loan category:    
Balance at beginning of period $ 2,835us-gaap_FinancingReceivableAllowanceForCreditLosses $ 3,013us-gaap_FinancingReceivableAllowanceForCreditLosses
Charge-offs (353)us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs (183)us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
Recoveries 37us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery 11us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery
Provision 420us-gaap_ProvisionForLoanLeaseAndOtherLosses 359us-gaap_ProvisionForLoanLeaseAndOtherLosses
Balance at the end of period 2,939us-gaap_FinancingReceivableAllowanceForCreditLosses 3,200us-gaap_FinancingReceivableAllowanceForCreditLosses
One-to four-family residential [Member]    
Activity in the allowance for loan losses by loan category:    
Balance at beginning of period 402us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
844us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
Charge-offs (12)us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
(108)us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
Recoveries    9us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
Provision 84us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
254us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
Balance at the end of period 474us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
999us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_Residential1To4FamilyRealEstateMember
Commercial real estate [Member]    
Activity in the allowance for loan losses by loan category:    
Balance at beginning of period 826us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
852us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
Charge-offs (193)us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
  
Recoveries      
Provision 199us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
(7)us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
Balance at the end of period 832us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
845us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialRealEstateMember
Construction [Member]    
Activity in the allowance for loan losses by loan category:    
Balance at beginning of period 784us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
604us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
Charge-offs    (75)us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
Recoveries 37us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
  
Provision (73)us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
29us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
Balance at the end of period 748us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
558us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_ConstructionLoansMember
Home equity lines of credit [Member]    
Activity in the allowance for loan losses by loan category:    
Balance at beginning of period 62us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
125us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
Charge-offs (147)us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
  
Recoveries      
Provision 151us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
12us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
Balance at the end of period 66us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
137us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_HomeEquityMember
Commercial business [Member]    
Activity in the allowance for loan losses by loan category:    
Balance at beginning of period 643us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
452us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
Charge-offs      
Recoveries    2us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
Provision 90us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
72us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
Balance at the end of period 733us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
526us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_CommercialLoanMember
Other [Member]    
Activity in the allowance for loan losses by loan category:    
Balance at beginning of period 9us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
9us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
Charge-offs (1)us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
  
Recoveries      
Provision (2)us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
(9)us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
Balance at the end of period 6us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= mgyr_FinancingReceivableOtherMember
  
Unallocated [Member]    
Activity in the allowance for loan losses by loan category:    
Balance at beginning of period 109us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_UnallocatedFinancingReceivablesMember
127us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_UnallocatedFinancingReceivablesMember
Charge-offs      
Recoveries      
Provision (29)us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_UnallocatedFinancingReceivablesMember
8us-gaap_ProvisionForLoanLeaseAndOtherLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_UnallocatedFinancingReceivablesMember
Balance at the end of period $ 80us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_UnallocatedFinancingReceivablesMember
$ 135us-gaap_FinancingReceivableAllowanceForCreditLosses
/ us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis
= us-gaap_UnallocatedFinancingReceivablesMember