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How long will it take an investment of $9,000 to double, if the investment earns interest at the...

Question:

How long will it take an investment of $9,000 to double, if the investment earns interest at the rate of 7% compounded continuously?

Compound Interest

Continuously compounding accounts are best modeled using an exponential function. If the amount invested is P at the r per year which is being compounded continuously, the amount accumulated after t years will be:


$$A=Pe^{rt} $$

Answer and Explanation:

The amount invested is {eq}P=\$9000 {/eq} and the amount accumulated is {eq}A=2*\$9000=\$18000 {/eq}. The rate of interest is {eq}r=0.07 {/eq} compounded continuously. Now, the time can be found as follows.


$$\begin{align} 9000e^{0.07t}&=18000\\ e^{0.07t}&=2\\ 0.07t&=\ln 2\\ t&\approx 9.90\text{ years} \end{align} $$


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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