Question

Sophie deposited money into an account in which interest is compoundedsemiannually at a rate of 2.4%. She made no other deposits or withdrawals and thetotal amount in her account after 11 years was $11,227.78. How much did shedeposit? Round answer to nearest whole number.

Answer 1

Given

Compounded semiannually

rate = 2.4%

time = 11 years

Future Value = $11,227.78

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \frac{A}{(1+\frac{r}{n})^{nt}}=\frac{P(1+\frac{r}{n})^{nt}}{(1+\frac{r}{n})^{nt}} \\ P=\frac{A}{(1+\frac{r}{n})^{nt}} \\ P=\frac{11227.78}{(1+\frac{0.024}{2})^{2(11)}} \\ P=\frac{11227.78}{1.012^{22}} \\ P=8636.20 \end{gathered}$

Rounding to the nearest whole number, the amount the she has deposited is $8636.