Question

With wages from a summer job you make a total of 13 deposits at $1,136 per month into a savings account earning 5.18% 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 17 years (dividends automatically are reinvested). The stocks are expected to provide an average annual return of 17.76% compounded monthly. When you finally sell the stocks, how much do you get?

Answer 1

Monthly rate = 5.18% / 12 = 0.431667%

Future value = Monthly rate * [(1 + r)^n- 1] / r

Future value = 1,136 * [(1 + 0.00431667)^13- 1] / 0.00431667

Future value = 1,136 * [1.057593 - 1] / 0.00431667

Future value = 1,136 * 13.342087

Future value = 15,156.61133

Value after 13 deposits are made is $15,156.61133

Monthly rate = 17.76% / 12 = 1.48%

Number of periods = 17 * 12 = 204

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

Future value = 15,156.61133 (1 + 0.0148)^204

Future value = 15,156.61133 * 20.026891

Future value = $303,539.81

You will get $303,539.81