Use the model A = Pe^rt to determine the average rate of return under continuous compounding. Round to thenearest tenth of a percent. Avoid rounding in intermediate steps.

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03-11-2022
Mathematics

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Use the model A = Pe^rt to determine the average rate of return under continuous compounding. Round to thenearest tenth of a percent. Avoid rounding in intermediate steps.

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TahmeedV438664 TahmeedV438664 · Answer 1 · 2022-11-03T12:30:17+01:00

Given

[tex]\begin{gathered} P=\$10,000 \\ A=\$14,296.88 \\ t=4 \\ \text{Find }r \end{gathered}[/tex][tex]\begin{gathered} A=Pe^{rt} \\ \text{Solve for }r \\ \frac{A}{P}=\frac{Pe^{rt}}{P} \\ \frac{A}{P}=\frac{\cancel{P}e^{rt}}{\cancel{P}} \\ e^{rt}=\frac{A}{P} \\ \ln e^{rt}=\ln \mleft(\frac{A}{P}\mright) \\ rt=\ln \mleft(\frac{A}{P}\mright) \\ r=\frac{\ln \mleft(\frac{A}{P}\mright)}{t} \\ \\ \text{Substitute the following values} \\ r=\frac{\ln \mleft(\frac{14296.88}{10000}\mright)}{4} \\ r=0.089364\rightarrow8.9364\% \\ \\ \text{Round to tenth of a percent} \\ r=8.9\% \end{gathered}[/tex]

Therefore, the average rate of return under continous compounding is approximately 8.9%.