Question

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

A) $ 9000
B) $ 11,200
C) $ 12,125
D) $ 13,550

Answer 1

This Question makes some sense if your adding the 3.2% Interest to get 13,987.17 it would have to be B

Answer 2

Option B - $ 11,200

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

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

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
`r=(0.032)/(2)=0.016`

Time became
`t=2*7=14`

Substitute in the formula,

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

`13987.17=P(1+0.016)^(14)`

`13987.17=P(1.016)^(14)`

`13987.17=P* 1.2488`

`P=(13987.17)/(1.2488)`

`P=11199.99`

Approximately P=$11200

Therefore, Option B is correct.