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Your wife can take $8,300 now, or $400 a month from age 60 to death.
Your wife would essentially receive the same $8,300 within 1.72 years of taking her benefit, so in the end she will get more from holding off until retirement.
Realistically, the $8,300 today will not grow by much in the marketplace. Rates are very low, so there's little incentive to get the money now and watch it appreciate
If you do a simple calculation and compare the payment option vs the lump sum, you will see that the payment option is more attractive.
Let's just assume that your wife lives to age 65. The present value of the annuity is $21,821 assuming a 5% ROI. That's over two times -nearly three times - the present value of $8,300 which is, $8,300
If your wife lives to age 70, the present value skyrockets to over $38,000.
Clearly taking the annuity, provided that your wife is healthy and expects to live well into her retirement, is the better bet.
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