Answer:
Option B - $ 11,200
Step-by-step explanation:
Given : Sophie deposited money into an account in which interest is compounded semiannually at a rate of 3.2%. She made no other deposits or withdrawals and the total amount in her account after 7 years was $13,987.17.
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 = $13,987.17
Rate = 3.2%=0.032
Time = 7 years
Compounded semiannually,
Rate became [tex]r=\frac{0.032}{2}=0.016[/tex]
Time became [tex]t=2\times7=14[/tex]
Substitute in the formula,
[tex]A=P(1+r)^t[/tex]
[tex]13987.17=P(1+0.016)^{14}[/tex]
[tex]13987.17=P(1.016)^{14}[/tex]
[tex]13987.17=P\times 1.2488[/tex]
[tex]P=\frac{13987.17}{1.2488}[/tex]
[tex]P=11199.99[/tex]
Approximately P=$11200
Therefore, Option B is correct.
