Compound Interest Rates

Question

Compute the annual compound interest rate required to double the size of a debt in 11 years. 

Round your answer to the nearest tenth of a percent. 

Answer 1

Allie, here's how to do this type of question.

The compound interest formula is: A = P(1 + i/100)ⁿ

Plug in the given values: 2P = P(1 + i/100)¹¹ [letting the initial debt be P

2 = (1 + i/100)¹¹

ln 2 = 11 log(1 + i/100) [taking logs to base e on both sides

ln(1 + i/100) = ln 2 / 11

ln(1 + i/100) = 0.063

1 + i/100 = 1.065

i/100 = 0.065

i = 6.5% per year