Question

You can afford monthly deposits of $90 into an account that pays 2.7% compounded monthly. How long will it be until you have $7,700 to buy a boat?

Type the number of months:____

(round to the next-higher month if not exact.)

Answer 1

P = Monthly payment = $90

r = monthly interest rate = 2.7%/12 = 0.225%

Let n = number of months

Amount required = $7,700

Therefore, amount required can be calculated using the below formula

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

$7,700 = $90 * [(1+0.225%)^n - 1] / 0.225%

$17.325 = $90 * [(1.00225)^n - 1]

(1.00225)^n - 1 = 0.1925

(1.00225)^n = 1.1925

n = log(1.1925) / log(1.00225)

n = 0.07645838771 / 0.00097606492

n = 78.3333015492

Therefore, it will take 79 months to buy a boat