A financial institution offers a "double-your-money" savings account in which you will have $2 in 9 years for every dollar you invest today. What annual interest rate does this account offer?

Question

Please specify your answer in decimal terms and round your answer to the nearest thousandth (e.g., enter 12.3 percent as 0.123).

Answer 1

In order to calculate the annual interest rate offered by the account, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)^Number of Years

Given that the account doubles the money invested in 9 years, we can set up the equation as follows:

2 = 1 * (1 + Interest Rate)^9

To find the interest rate, we need to isolate it on one side of the equation. We can do this by taking the 9th root of both sides:

(1 + Interest Rate) = 2^(1/9)

Next, we subtract 1 from both sides:

Interest Rate = 2^(1/9) - 1

Using a calculator, we find that 2^(1/9) is approximately 1.082576175, and subtracting 1 gives us approximately 0.082576175.

Therefore, the annual interest rate offered by the account is approximately 0.083.