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Question

# Investigate the difference between compounding annually and simple interest. Round to the nearest cent. Find the interest for a 3-year CD for \$5,000 at an interest rate of 2.5%, compounded annually.

Solution

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We have to Find the interest for a 3-year CD for $5,000$ USD at an interest rate of $2.5\%$, compounded annually.First we have to calculate balans and then we calculate interest like a difference betwen balanse and principal. We calculate balanse using a equation,

\begin{align*} B=P\left(1+\dfrac{r}{n}\right)^{n\cdot t} \end{align*}

where is $P$ principal, $r$ is interest rate, $n$ is number of times interest is compounded annualy, $t$ is time in number of year. How is $5000$, $r=0.025$, $n=1$, and $t=3$, so we calculte,

\begin{align*} B=5000\left(1+\dfrac{0.025}{1}\right)^{3}=5384.45\,\,\text{USD} \end{align*}

And interest is,

\begin{align*} I=B-P=5384.45-5000=384.45\,\,\text{USD} \end{align*}

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