Question

Sophie deposited money into an account in which interest is compoundedsemiannually at a rate of 4.4%. She made no other deposits or withdrawals and thetotal amount in her account after 12 years was $10,336.84. How much dd shedeposit? Round answer to nearest whole number.

Answer 1

Step 1

State the formula for the amount of compound interest

$A=P(1+\frac{r}{n})^{nt}$

where;

$\begin{gathered} P=deposited\text{ money} \\ r=rate=\frac{4.4}{100}=0.044 \\ t=12years \\ n=2 \\ A=10336.84 \end{gathered}$

Step 2

Find how much she deposited

$10336.84=P(1+\frac{0.044}{2})^{2\times12}$$\begin{gathered} 10336.84=P(1.022)^{24} \\ \frac{\begin{equation*}P(1.022)^{24}\end{equation*}}{(1.022)^{24}}=\frac{10336.84}{(1.022)^{24}} \\ P=\text{ \ 6131.49382} \\ P\approx\text{ \ 6131} \end{gathered}$

Hence the amount she deposited to the nearest whole number is;

$P=\text{\ 6131}$