Final amount with compound interest is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
P is the principal amount
r is the interest rate in decimal form (%/100)
n is the number o times compounded
t is the time in years
For the given situation:
[tex]\begin{gathered} P=5,000 \\ r=\frac{2.25}{100}=\text{0}.0225 \\ n=4(quarterly) \\ t=5 \\ \\ A=5,000(1+\frac{0.0225}{4})^{4\cdot5} \\ \\ A=5,000(1+\frac{0.0225}{4})^{20} \\ \\ A\approx5,593.60 \end{gathered}[/tex]
Then, the balance after 5 years (final amount) is $5,593.60
