Question

Annual Percentage Yield Find the annual percentage yield for an investment that earns 8% per year, compounded monthly.

Short answer

The annual percentage yield is 8.3%.

Step-by-step solution

Step 1. Given.

$r=\mathrm{interest}\mathrm{rate}=8\%=0.08$.

$n=\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{times}\mathrm{compounded}\mathrm{in}\mathrm{a}\mathrm{year}=12$.

Because, interest is compounded monthly.

Step 2. To determine.

We have to find the annual percentage yield.

Step 3. Calculation

Let, $APY=$Annual percentage yield.

Using the annual percentage yield formula:$APY={\left(1+\frac{r}{n}\right)}^n-1$

Then we plug the values and find APY.

$$\begin{gathered} APY={\left(1+\frac{r}{n}\right)}^n-1 \\ APY={\left(1+\frac{0.08}{12}\right)}^{12}-1 \\ APY=1.08299950681-1 \\ APY=0.08299950681 \\ APY=8.299950681\% \\ APY\approx 8.3\% \end{gathered}$$

Hence, the annual percentage yield is 8.3%.