Question

Ryan wants to accumulate at least $55,000 by depositing $1,800 at the end of every month into a fund that earns interest at 5.50% compounded monthly.

a. How many deposits does he need to make to reach his goal?

b. How long will it take Ryan to reach his goal?

Answer 1

a). FVA = Annuity x [{1 - (1 + r)^-n} / r]

$55,000 = $1,800 x [{1 - (1 + 0.055/12)^-n} / (0.055/12)]

30.56 = [{1 - (1.0046)^-n} / 0.0046]

0.1400 = 1 - (1.0046)^-n}

(1.0046)^-n = 0.85995

-n[ln(1.0046)] = ln(0.85995)

-n = ln(0.85995) / ln(1.0046)

-n = -0.1509 / 0.0046

n = 33

So, it will take 33 deposits to reach the goal.

b). It will take 2.75 years(33/12) to reach the goal.