Answer :
Given data:
Principal (starting amount) = $10, 000
Interest rate compounded quarterly = 3.6% = 0.036
The modeled account balance is
[tex]A(t)=a(1+\frac{r}{k})^{kt}[/tex]SOLUTION A.
The values that should be used for a, r and k are:
[tex]\begin{gathered} a=\text{ \$10,000} \\ r=3.6\text{ \% = 0.036} \\ k=\text{ 4 (compounded quartely)} \end{gathered}[/tex]SOLUTION B
The money Hailey will have in the account in 9 years would mean that t = 9 years. Hence,
[tex]\begin{gathered} A(t)=10,000(1+\frac{0.036}{4})^{4\times9} \\ A(t)=10,000(1+0.009)^{36}_{} \\ A(t)=10,000(1.009)^{36} \\ A(t)=\text{ \$}13806.45 \end{gathered}[/tex]SOLUTION C
The annual percentage yield (APY) can be calculated using the formula below
[tex]\begin{gathered} \text{APY}=(1+\frac{r}{n})^n-1 \\ APY=(1+\frac{0.036}{4})^{^4}-1 \\ APY=(1+0.009)^4-1 \\ APY=(1.009)^4-1 \\ APY=1.0365^{}-1 \\ APY=0.03649 \\ APY=3.649\text{ \%} \end{gathered}[/tex]