Answer:
7.23%.
Step-by-step explanation:
We are asked to find APY (Annual Percentage Yield) to the nominal rate of 7% compounded semiannually.
We will use annual percentage yield formula to solve our given problem.
[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
Let us convert 7% into decimal form.
[tex]7\%=\frac{7}{100}=0.07[/tex]
Semiannually means two times per year.
[tex]APY=(1+\frac{0.07}{2})^{2}-1[/tex]
[tex]APY=(1+0.00583333)^{12}-1[/tex]
[tex]APY=(1.00583333)^{12}-1[/tex]
[tex]APY=1.0722900804298071-1[/tex]
[tex]APY=0.0722900804298071[/tex]
[tex]APY\approx 0.0723[/tex]
Let us convert 0.0723 into percentage by multiplying with 100.
[tex]0.0723\times 100=7.23\%[/tex]
Therefore, annual percentage yield would be 7.23%.
