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FAIR VALUE DISCLOSURES (Schedule of Assets Measured at Fair Value on a Recurring Basis) (Details) (USD $)
In Thousands, unless otherwise specified
Sep. 30, 2014
Sep. 30, 2013
Fair value measured on recurring basis:    
Securities available for sale $ 12,070us-gaap_AvailableForSaleSecurities $ 15,774us-gaap_AvailableForSaleSecurities
Obligations of U.S. government agencies Mortgage backed securities - residential [Member]    
Fair value measured on recurring basis:    
Securities available for sale 1,295us-gaap_AvailableForSaleSecurities
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentAgenciesDebtSecuritiesResidentialMortgageBackedSecuritiesMember		 1,556us-gaap_AvailableForSaleSecurities
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentAgenciesDebtSecuritiesResidentialMortgageBackedSecuritiesMember
Obligations of U.S. government-sponsored enterprises Mortgage backed securities - residential [Member]    
Fair value measured on recurring basis:    
Securities available for sale 10,369us-gaap_AvailableForSaleSecurities
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesResidentialMortgageBackedSecuritiesMember		 9,401us-gaap_AvailableForSaleSecurities
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesResidentialMortgageBackedSecuritiesMember
Obligations of U.S. government-sponsored enterprises Mortgage backed securities -commercial [Member]    
Fair value measured on recurring basis:    
Securities available for sale   4,002us-gaap_AvailableForSaleSecurities
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesCommercialMortgageBackedSecuritiesMember
Private label mortgage-backed securities-residential [Member]    
Fair value measured on recurring basis:    
Securities available for sale 406us-gaap_AvailableForSaleSecurities
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember		 815us-gaap_AvailableForSaleSecurities
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember
Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 2 [Member]    
Fair value measured on recurring basis:    
Securities available for sale 12,070us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember		 15,774us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember
Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 2 [Member] | Obligations of U.S. government agencies Mortgage backed securities - residential [Member]    
Fair value measured on recurring basis:    
Securities available for sale 1,295us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentAgenciesDebtSecuritiesResidentialMortgageBackedSecuritiesMember		 1,556us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentAgenciesDebtSecuritiesResidentialMortgageBackedSecuritiesMember
Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 2 [Member] | Obligations of U.S. government-sponsored enterprises Mortgage backed securities - residential [Member]    
Fair value measured on recurring basis:    
Securities available for sale 10,369us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesResidentialMortgageBackedSecuritiesMember		 9,401us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesResidentialMortgageBackedSecuritiesMember
Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 2 [Member] | Obligations of U.S. government-sponsored enterprises Mortgage backed securities -commercial [Member]    
Fair value measured on recurring basis:    
Securities available for sale   4,002us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesCommercialMortgageBackedSecuritiesMember
Fair Value, Measurements, Recurring [Member] | Fair Value, Inputs, Level 2 [Member] | Private label mortgage-backed securities-residential [Member]    
Fair value measured on recurring basis:    
Securities available for sale $ 406us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember		 $ 815us-gaap_AvailableForSaleSecurities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
/ us-gaap_FairValueByMeasurementFrequencyAxis
= us-gaap_FairValueMeasurementsRecurringMember
/ us-gaap_MajorTypesOfDebtAndEquitySecuritiesAxis
= us-gaap_MortgageBackedSecuritiesIssuedByPrivateEnterprisesMember