Respuesta :
Solution
Step-by-step 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
[tex]A=P(1+r)^t[/tex]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
[tex]\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=\frac{11719.04}{1.26174} \\ P=9287.9991 \end{gathered}[/tex]Therefore the amount deposited = 9287.9991
Approximately = 9288
