Question

22. You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $170,000? Round fractional months up.

a. 31

b. 28

c. 34

d. 23

e. 22

Answer 1

P = Monthly investment = $5,000

r = Monthly interest rate = 18%/12 = 1.5%

FV = Future Value = $170,000

Let n = number of months

FV = [P * [(1+r)^n - 1] / r] * (1+r)

$170,000 = [$5,000 * (1+1.5%)^n - 1] / 1.5%] * (1+1.5%)

$167,487.685 = $33,333.333333* (1.015)^n - $333,333.333333

$333,333.333333 * (1.015)^n = $500,821.018

(1.015)^n = 1.50246305

n = log(1.50246305) / log (1.015)

n = 0.1768038 / 0.00646604225

n = 27.3434341

n = 28 months

Therefore, it will take 28 months to reach goal of $170,000

Option b is correct