Question

Sophie deposited money into an account in which interest is compoundedsemiannually at a rate of 3.5%. She made no other deposits or withdrawals and thetotal amount in her account after 15 years was $24,484.29. How much did shedeposit? Round answer to nearest whole number.

Answer 1

Solution:

Given:

$\begin{gathered} A=\text{ \ 24,484.29} \\ t=15yrs \\ r=3.5\text{ \%}=\frac{3.5}{100}=0.035 \\ n=2\text{ \lparen semiannually\rparen} \end{gathered}$

Using the compound interest formula for calculating the amount,

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

Hence, substituting the given values into the formula to get the principal,

$\begin{gathered} 24484.29=P(1+\frac{0.035}{2})^{2\times15} \\ 24484.29=P(1+0.0175)^{30} \\ 24484.29=P(1.0175)^{30} \\ 24484.29=P\times1.6828 \\ \frac{24484.29}{1.6828}=P \\ P=14549.7 \\ To\text{ the nearest whole number,} \\ P\approx\text{ \ 14,550} \end{gathered}$

Therefore, to the nearest whole number, Sophie deposited $14,550