We are given the following information
Deposited amount = P = $9000
Interest rate = r = 6.6% = 0.066
Compounding interval = n = quarterly = 4
Number of years = t = 13
We are asked to find the accumulated amount (or ending balance)
Recall that the compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{n\cdot t}[/tex]Where
A = Accumulated amount (or ending balance)
P = Deposit amount
r = Interest rate in decimal
n = Number of compounding in a year
t = Number of years
Now let us substitute the given values into the above formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{n\cdot t} \\ A=9000\cdot(1+\frac{0.066}{4})^{4\cdot13} \\ A=9000\cdot(1+0.0165)^{52} \\ A=9000\cdot(1.0165)^{52} \\ A=\$21077.85 \end{gathered}[/tex]Therefore, after 13 years, the account balance will be $21077.85
