Question 334685
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The formula for the Future Value, *[tex \Large A] of an investment *[tex \Large P] at *[tex \Large r] rate of interest for *[tex \Large t] years compounded continuously is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ Pe^{rt}]


Substitute what you know:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 60,000\ =\ 20,000e^{20r}]


A little algebra:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ e^{20r}\ =\ 3]


Take the natural log of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(e^{20r}\right)\ =\ \ln(3)]


Apply the laws of logarithms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 20r\ln(e)\ =\ \ln(3)]


But *[tex \Large \ln(e)\ =\ 1], so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ r\ =\ \frac{\ln(3)}{20}]


The rest is just calculator work.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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