Explanation
From the given question
We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%
The formula is given by
[tex]A(t)=a(1+\frac{r}{k})^{kt}[/tex]
Part A
[tex]\begin{gathered} a=initial\text{ deposit= \$8000} \\ \\ k=number\text{ of times compounded in a year = 4} \\ \\ r=2.8\text{ \% =0.028} \\ \\ \end{gathered}[/tex]
part B
the amount in the account after 7 years will be
[tex]\begin{gathered} A(t)=8000(1+\frac{0.028}{4})^{4\times7} \\ \\ A(7)=\text{ \$}9725.57\text{ } \end{gathered}[/tex]
The amount that will be in the account after 7 years will be $9725.57
Part C
APY is given by
In our case we have
[tex]\begin{gathered} APY=(1+\frac{r}{k})^k-1 \\ APY=\left(1+\frac{0.028}{4}\right)^4\:-1 \\ APY=1.02829-1 \\ APY=0.02829 \end{gathered}[/tex]
Hence, we will have the APY as
[tex]\begin{gathered} APY=0.02829\times100\text{ \% } \\ APY=2.829\text{ \%} \end{gathered}[/tex]
Hence, the APY is 2.829%
