4. It is estimated that you pay $2,000 per year into the Social Security System (FICA) over your 40-year work span. For simplicity, assume that your annuity of $2,000 per year, starting with your 26th birthday and continuing through your 65th birthday. The deposit is done at the end of the year. However, the government decides to provide you the annual withdrawal only after the end of 67th birthday. If the government interest rate is 6% per year, what equal annual withdrawal you can do, if you expect to live till the end of 86th birthday

$30,320.94

Explanation:

first we must determine the future value of your social security contributions:

when you are 65, your contributions will be worth = $2,000 x 154.762 (FV annuity factor, 6%, 40 periods) = $309,524

now we must determine the value of the contributions when you are 67:

FV = $309,524 x (1 + 6%)² = $347,781.17

you expect to live 20 more years, so we need to determine the annuity payment:

annuity payment = principal / PV annuity factor, 6%, 20 periods = $347,781.17 / 11.470 = $30,320.94

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