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First of all full retirement age is age 66 for you not age 65 (it wull actually gradually go up to age 67 eventually). You can claim a retroactive benefits payment if you file for retirement benefits after you reach full retirement age (FRA). So if you file between age 66½ and 70, you can get up to six months of payments in a lump sum. The drawback is that since you waited until age 67, you gain an 8% credit per year that you delay until age 70. Between your FRA and age 70, your unclaimed benefits rise in value at the rate of 8% a year, thanks to delayed retirement credits. If you file for your retirement benefit at age 70, for example, you will qualify for the highest possible benefit—payments that are 32% higher than your benefit at age 66 and 76% higher than at age 62. So to answer your question, yes but you will lose your 8% credit increase and you can only receive 6 months in back benefits.
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