Question

What annual rate of interest compounded annually is required to double an investment in 6 years?

Answer 1

Approximately 12.25%

Explanation:

The compound interest formula is:

Final balance = Principal * (1 + interest rate/number of times interest compounded per year)^(number of times interest compounded per year * years elapsed)

If we want our final balance to be twice our principal, our formula looks like:

`2P = P * (1 + (r)/(1))^(1*6)`

We can divide our principal from both sides to get the following equation:

`2 = (1 + (r)/(1))^(6)`

Since anything divided by 1 is itself, we can simplify a little further to:

`2 = (1 + r)^(6)`

Now, we need to solve for r. We can start by taking the sixth root of both sides.

`\sqrt[6]{2} = 1 + r`

Then subtract 1 from both sides:

`\sqrt[6]{2} -1 = r`

Finally, we can use a calculator to get a decimal approximation:

0.1225 ≅ r