Question

In 2012 the maximum Social Security deposit by an individual was $8,386.75. Suppose you are 33 and make a deposit of this amount into an account at the end of each year. How much would you have (to the nearest dollar) when you retire if the account pays 4% compounded annually and you retire at age 65?

Answer 1

Here, the deposits will be same every year, so it is an annuity. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $8386.75, r is the rate of interest = 4% and n is the time period = 65 - 33 = 32

Now, putting these values in the above formula, we get,

FVA = $8386.75 * ((1 + 4%)³² - 1 / 4%)

FVA = $8386.75 * ((1 + 0.04)³² - 1 / 0.04)

FVA = $8386.75 * ((1.04)³² - 1 / 0.04)

FVA = $8386.75 * ((3.50805874685 - 1 / 0.04)

FVA = $8386.75 * (2.50805874685/ 0.04)

FVA = $8386.75 * 62.70146867

FVA = $525861.54

So, we will have $525861.54 when we retire.