Question

Jon has $5,000 to invest in a savings account that has interest compounded annually. If he wants his money to double in eight years, what percent must the interest rate be on the account?

Answer 1

Use A = P(1+r)^n with A = 2P and n = 8:
(1 + r)^8 = 2 ⇒ 1 + r = 2^{1/8} ⇒ r = 2^{1/8} − 1 ≈ 0.0905077.

So the annual interest rate must be about 9.05%.