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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

2 Answers

2 votes
This Question makes some sense if your adding the 3.2% Interest to get 13,987.17 it would have to be B
User RANGER
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Answer:

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.

User Parthasarathy B
by
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