Good afternoon Linda,
I'm Doug, and my goal is to provide you with excellent service today.
Yes, indeed, as you are over the age of 66 you are eligible to file a retroactive retirement benefit application with social security. You may file retroactively up to 6 months. However as your benefit finally reached its maximum level on your 70th birthday, if you retire this month (June 2016) and ask for back benefits to January, while you will get the 6 months retroactive benefits, your lifetime benefit from here on out will be about 2.3% less than if you just asked for it retroactive to your 70th birthday month.
So, if you want to maximize your retirement benefit going forward, while you can ask for retroactive benefits going back up to 6 months, you might be better off asking for benefits only going back to when you turned 70.
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I wish you and yours the best in 2016,