Question

With wages from a summer job you make a total of 15 deposits at $518 per month into a savings account earning 5.85% compounded monthly. At the time of the last deposit, you close the savings account and invest all the money in stocks with the intention of leaving the stocks alone for the subsequent 15 years (dividends automatically are reinvested). The stocks are expected to provide an average annual return of 22.03% compounded monthly. When you finally sell the stocks, how much do you get?

Answer 1

The amount is computed as follows:

Value in 15 years is computed as follows:

Future value = Monthly payment x [ [ (1 + r)ⁿ – 1 ] / r ]

r = 5.85% / 12

= 0.4875%

So, the amount will be as follows:

= $ 518 x [ [ (1 + 0.004875)¹⁵ - 1 ] / 0.004875 ]

= $ 518 x 15.52284821

= $ 8,040.835375

Value in 30 years will be as follows:

Future value = Present value x (1 + r)ⁿ

r will be as follows:

= 22.03% / 12

= 1.835833333%

n will be as follows:

= 15 x 12

= 180

So, the amount will be as follows:

= $ 8,040.835375 x (1 + 0.01835833333)¹⁸⁰

= $ 8,040.835375 x 26.43089482

= $ 212,526.49