Question

Sophie deposited money into an account in which interest is compoundedsemiannually at a rate of 2.6%. She made no other deposits or withdrawals and thetotal amount in her account after 9 years was $11,719.04. How much did shedeposit? Round answer to nearest whole number. Do not include units in theanswer.

Answer 1

Explanation:

Given : Sophie deposited money into an account in which interest is compounded semiannually at a rate of 2.6%. She made no other deposits or withdrawals and the total amount in her account after 9 years was $11,719.04

To find : The money deposited

Solution :

Formula to find Compound interest is

`A=P(1+r)^t`

P is the principle value

Where A is the amount = $11,719.04

Rate = 2.6%=0.026

Time = 9 years

Compounded semiannually

Rate became = 0.026/2 =0.013

time became = 2 x 9 = 18

`\begin{gathered} A=P(1+r)^t \\ 11,719.04=P(1+0.013)^(18) \\ 11,719.04=P(1.013)^(18) \\ 11,719.04=1.26174P \\ P=(11719.04)/(1.26174) \\ P=9287.9991 \end{gathered}`

Therefore the amount deposited = 9287.9991

Approximately = 9288