Question

Justin is going to invest $90,000 and leave it in an account for 19 years. Assuming

the interest is compounded quarterly, what interest rate, to the nearest hundredth of
a percent, would be required in order for Justin to end up with $216,000?

Answer 1

4.63%

Explanation:

You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.

Compound interest

The formula for the balance of an account earning compound interest is ...

A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

Application

Filling in the given values, we can solve for r:

216000 = 90000(1 +r/4)^(4·19)

2.4 = (1 + r/4)^76 . . . . . divide by 90,000

2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root

(2.4^(1/76) -1) = r/4 . . . . . . subtract 1

r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%

The required interest rate is about 4.63%.