### Home > CCA2 > Chapter 7 > Lesson 7.1.6 > Problem7-95

7-95.

What interest rate (compounded annually) would you need to earn in order to double your investment in 15 years?

Compound interest is exponential.
Use the general equation $y=ab^x$ where
$a=$ initial investment,
$b=$ multiplier,
$x=$ number of years, and
$y=$ total investment.

If you invest $100 initially, you will have$200 when it has doubled.
Input the values into the equation.

$200=100(b)^{15}$

Divide both sides by 100 and take the 15th root of both sides

(or raise both sides to the $\frac{1}{15}$ power.)

$b=1.04729$

Convert the multiplier to an interest rate, I.
Since this is an increasing exponential function, subtract 1 before converting to a percent.

$I\approx0.04729\approx4.73\%$