Question

With wages from a summer job you make a total of 14 deposits at $784 per month into a savings account earning 8.71% 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 21 years (dividends automatically are reinvested). The stocks are expected to provide an average annual return of 16.15% compounded monthly. When you finally sell the stocks, how much do you get?

Answer 1

FV of annuity = C x [(1+r) ⁿ- 1/r]

C = Periodic cash deposit = $ 784

r = Rate of interest = 0.0871/12 = 0.007258333 p.m.

n = Number of periods = 14

FV = $ 784 x [(1+0.007258333)¹⁴ – 1/0.007258333]

    = $ 784 x [(1.007258333)¹⁴ – 1/0.007258333]

= $ 784 x [(1.10655286159014 – 1)/0.007258333]

= $ 784 x (0.10655286159014/0.007258333)

= $ 784 x 14.680073453524

= $ 11,509.1775875628 or $ 11,509.18

FV of stock = PV x (1+r) ⁿ

r = 0.1615/12 = 0.013458333

n = 21 x 12 = 252

FV = $ 11,509.18 x (1+0.013458333)²⁵²

      = $ 11,509.18 x (1.013458333)²⁵²

      = $ 11,509.18 x 29.045996721488

      = $ 334,295.604547016 or $ 334,295.60

Selling the stock finally will give $ 334,295.60