If you invest your $9000 at an annual interest rate of 4%, compounded monthly, how long will it take (in years) before you can purchase the car?

Question

FULL QUESTION: Suppose that you want to purchase a used car for $12000. You currently have $9000. If you invest your $9000 at an annual interest rate of 4%, compounded monthly, how long will it take (in years) before you can purchase the car?

**Answer is apparently not 7.2

Answer 1

The basic equation to use is

A = P * (1 + r)^t

where P is the original principal, r is the interest rate per period, and t is the number of periods. Here we have 4% annual rate compounded monthly so

r = .04 / 12

and t is in months.

So we need to solve

12,000 = 9000 * (1 + (.04/12))^t

or

(1.003333)^t = 12000 / 9000 = 4/3

or, taking the logarithm of both sides

t * log(1.003333) = log(4/3)

from which

t = 86.45 or about 7 years and 3 months.