We can find the balance at the end of the 13 years by means of the following formula:
[tex]FV=A\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}[/tex]
Where FV is the future value of the annuity by the end of t years, A is the annuity, n is the number of times interest is compounded per year (quarterly) and t is the time.
By replacing 550 for A, 4 for n, 0.048 for r (4.8%) and 13 for t into the above formula, we get:
[tex]FV=550\frac{(1+\frac{0.048}{4})^{4(13)}-1}{\frac{0.048}{4}}=39392[/tex]
Then, by the end of the 13 years, the annuity will hold $39392
