### Home > A2C > Chapter 8 > Lesson 8.1.6 > Problem8-96

8-96.

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.

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

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

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

$200 = 100\left(b\right)^{15}$

$b = 1.04729$

$I ≈ 0.04729 ≈ 4.73%$