Question

Investment A offers an 8% return compounded semiannually, and Investment B offers a 7.75% return compounded continuously. Which investment has a higher rate of return over a 4-year period?

Solution

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Compound Interest Formula

A=P(1+rm)mtA = P\bigg(1 + \frac{r}{m}\bigg)^{mt}

Let PP be the investment in both the cases. Then, the accumulated amount for investment AA with r=0.08, m=2r = 0.08,\ m = 2 and t=4t = 4 is

A=P(1+0.082)(2)(4)=P(1.04)81.36857P\begin{align*} A & = P\bigg(1 + \frac{0.08}{2}\bigg)^{(2)(4)}\\ & = P(1.04)^{8}\\ & \approx 1.36857P \end{align*}

Continuous Compound Interest Formula

A=PertA = Pe^{rt}

The accumulated amount for investment BB with r=0.0775r = 0.0775 and t=4t = 4 is

A=Pe(0.0775)(4)=Pe0.311.363425P\begin{align*} A & = Pe^{(0.0775)(4)}\\ & = Pe^{0.31}\\ & \approx 1.363425P \end{align*}

Therefore, investment AA has a higher rate of return.

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