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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:


$$A=Pe^{rt} $$

Answer and Explanation:

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.


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


Learn more about this topic:

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Exponential Growth: Definition & Examples

from High School Algebra I: Help and Review

Chapter 6 / Lesson 10
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