I have looked over the internet for this answer but to no avail. Say, I take social security at age 66 and my wife files for social security at age 62 on my benefit (I believe she will receive 37.5% of my benefit, 1/2 - a percent deduction for early filing). My question is; If I die will she receive my FRA, i.e. the amount I was receiving or a reduced amount of my FRA due to the fact she started taking hers on my benefit at age 62? Example: My FRA at 66 is $2000, at 62 she will receive $750. If I die before her will she receive a reduced amount of the $2000 or the $2000? Her FRA because she didn't work much throughout life is $350.
Spousal benefits and widow's benefits are separate benefits. Your wife's widow's benefit rate would be determined based on her age at the time she becomes eligible for that benefit, regardless of whether or not she filed for reduced spousal benefits.
Using your example, if your full retirement age rate (PIA) is $2000, your wife could get an unreduced spousal benefit of $1000 if she waits until full retirement age to start drawing. But, if she's entitled to a PIA of $350 on her own record, she would actually get the $350 from her own record and $650 from your record. If she files at age 62, both benefits would be reduced. Her own benefit would be reduced by 25% to 30%, and her spousal benefit would be reduced by 30% to 35%, depending on her year of birth. Thus, in your example, her combined benefit rate at age 62 would be between around $667 & $717 depending on her year of birth.
Regardless of when your wife starts drawing retirement and spousal benefits, though, if you die after she has already reached full retirement age (FRA), she would receive your full benefit rate as a widow. And, if you wait until age 70 to start drawing you benefits, she could receive your full age 70 rate inclusive of the delayed retirement credits you earned. If you die before she reaches full retirement age, your wife could either wait until FRA to get an unreduced widow's benefit, or start drawing it early at a reduced rate.
You and your wife may want to consider using the maximization software available on this website in order to explore all of your filing options and determine your best strategy.