Question

If you deposit $4,800 at the end of each of the next 15 years into an account paying 11.3 percent interest, how much money will you have in the account in 15 years? How much will you have if you make deposits for 30 years?

Answer 1

You can solve this question by using simply Future value Of an annuity factor formula i.e = [(1+i)ⁿ - 1]/i

i= interest rate

n= number of years

FVAF(15 years) = [(1+0.113)¹⁵ - 1]/ 0.113 = 3.9823/0.113 = 35.2413

Future value of this annuity after 15 years = 4800*35.2413 = $169,158.

FVAF(30 years) =  [(1+0.113)³⁰ - 1]/ 0.113 = 23.823/0.113 = 210.8233

Future value of this annuity after 30 years = 4800* 210.8233= $1,011,952.

Answer 2

Here we need to find the FVA. The equation to find the FVA is:

FVA = C{[(1 + r)^t – 1] / r}

FVA for 15 years = $4,800[(1.113¹⁵– 1) / .113] = $ 169,158.47

FVA for 30 years = $4,800[(1.113³⁰– 1) / .113] = $ 1,011,952.05

Notice that because of exponential growth, doubling the number of periods does not merely double the FVA