Solution:
The Annual Percentage Yield(APY) is expressed as
[tex]\begin{gathered} APY=(1+\frac{r}{n})^n-1 \\ where \\ r=period\text{ rate} \\ n=number\text{ of compoundimg periods} \end{gathered}[/tex]Given that
[tex]\begin{gathered} r=7.65\%=0.0765 \\ n=12\text{ \lparen compounded monthly\rparen} \end{gathered}[/tex]By substitution, we have
[tex]\begin{gathered} APY=(1+\frac{0.0765}{12})^{12}-1 \\ =0.07924 \\ \therefore \\ APY\approx0.079\text{ \lparen3 decimal places\rparen} \end{gathered}[/tex]Hence, we have
[tex]0.079[/tex]