# What interest rate, to the nearest tenth of a percent, is required for an investment subject to...

## Question:

What interest rate, to the nearest tenth of a percent, is required for an investment subject to continuous compounding to double in 10 years?

## Compound Interest

In continuous compounding, the amount is growing at all times. As such, we use an exponential model to find the amount accumulated at any time. The formula is:

$$A=Pe^{rt}$$

Let the initial investment be {eq}x {/eq} so that it doubles to {eq}2x {/eq} in {eq}10 {/eq} years. The rate can be found as follows.

\begin{align} xe^{10r}&=2x\\ e^{10r}&=2\\ 10r&=\ln2\\ r&\approx 6.9\% \end{align}\\