Question

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.

Answer 1

Given

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

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