If interest is compounded annually, what is the annual interest rate if an initial investment of doubles in 12 years?

Question

How do I find the annual interest rate

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that we want to use here for compound interest is

A = P(1 + r)^t

If the investment doubles in 12 years that means that

12P = P(1 + r)^12

2 = (1 + r)^12

r = (2)^(1/12) – 1

r = 0.05946

meaning that the interest rate here is about 5.95%

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Future Value = Present Value * (1 + interest rate)^years

 

2 = 1 * (1 + interest rate)¹²

 

2= (1 + interest rate)¹² ; solve for the interest rate by taking the 12 root of both sides

 

2^1/12 = (1 + interest rate) = 1.0594

interest rate  = 1.0594 - = .0594 or 5.94%