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

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