Given that the principal (P) is $8,788, time (T) is 4 years.
Let R be the annual rate of interest.
Given that the compounding is done 6 times a year, then the rate of interest per period and the number of periods is calculated as,
[tex]\begin{gathered} r=\frac{R}{6} \\ n=6\times T=6\times4=24 \end{gathered}[/tex]Consider the formula for amount (A) as,
[tex]A=P(1+\frac{r}{100})^n[/tex]Substitute the values and simplify,
[tex]\begin{gathered} 11490.08=8788(1+\frac{R}{600})^{24} \\ (1+\frac{R}{600})^{24}=\frac{11490.08}{8788} \\ 1+\frac{R}{600}=(1.3075)^{\frac{1}{24}} \\ 1+\frac{R}{600}=1.01123 \\ \frac{R}{600}=0.01123 \\ R\approx6.74 \end{gathered}[/tex]Thus, the annual interest rate of the account is 6.74% approximately.
