Given
Compounded semiannually
rate = 2.4%
time = 11 years
Future Value = $11,227.78
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \frac{A}{(1+\frac{r}{n})^{nt}}=\frac{P(1+\frac{r}{n})^{nt}}{(1+\frac{r}{n})^{nt}} \\ P=\frac{A}{(1+\frac{r}{n})^{nt}} \\ P=\frac{11227.78}{(1+\frac{0.024}{2})^{2(11)}} \\ P=\frac{11227.78}{1.012^{22}} \\ P=8636.20 \end{gathered}[/tex]Rounding to the nearest whole number, the amount the she has deposited is $8636.
