Question

Annual Percentage Yield Find the annual percentage yield for an investment that earns$5\frac{1}{2}\%$per year, compounded quarterly.

Short answer

The annual percentage yield is 5.6%.

Step-by-step solution

Step 1. Given.

$r=\mathrm{interest}\mathrm{rate}=5\frac{1}{2}\%=5.5\%=0.055\%$.

$n=\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{times}\mathrm{compounded}\mathrm{in}\mathrm{a}\mathrm{year}=4$.

Because, interest is compounded quarterly.

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.

$$\begin{gathered} APY={\left(1+\frac{r}{n}\right)}^n-1 \\ APY={\left(1+\frac{0.055}{4}\right)}^4-1 \\ APY=1.05614480918-1 \\ APY=0.05614480918 \\ APY=5.614480918\% \\ APY\approx 5.6\% \end{gathered}$$

Hence, the annual percentage yield is 5.6%.