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

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

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

\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

$A = Pe^{rt}$

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

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

Therefore, investment $A$ has a higher rate of return.

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