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

Given:

`\begin{gathered} A=\text{ \$24,484.29} \\ t=15yrs \\ r=3.5\text{ \%}=(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+(r)/(n))^(nt)`

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

`\begin{gathered} 24484.29=P(1+(0.035)/(2))^(2*15) \\ 24484.29=P(1+0.0175)^(30) \\ 24484.29=P(1.0175)^(30) \\ 24484.29=P*1.6828 \\ (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