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Amy deposits \(\$100\) into an account that pays \(8\%\) interest, compounded semiannually. She makes no other deposits

Expert replies
by Gmat_mission » Thu Nov 19, 2020 11:24 am

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Difficulty

Amy deposits \(\$100\) into an account that pays \(8\%\) interest, compounded semiannually. She makes no other deposits or withdrawals. Which of the following expresses the amount of money the account will contain in \(2\) years?

A. \(\$100 \cdot (1 + .04)^2\)

B. \(\$100 \cdot (1 + .04)^4\)

C. \(\$100 \cdot (1 + .04)^6\)

D. \(\$100 \cdot (1 + .08)^2\)

E. \(\$100 \cdot (1 + .08)^6\)

Answer: B

Source: Princeton Review
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Source: — Problem Solving |

Gmat_mission wrote:
Thu Nov 19, 2020 11:24 am
Amy deposits \(\$100\) into an account that pays \(8\%\) interest, compounded semiannually. She makes no other deposits or withdrawals. Which of the following expresses the amount of money the account will contain in \(2\) years?

A. \(\$100 \cdot (1 + .04)^2\)

B. \(\$100 \cdot (1 + .04)^4\)

C. \(\$100 \cdot (1 + .04)^6\)

D. \(\$100 \cdot (1 + .08)^2\)

E. \(\$100 \cdot (1 + .08)^6\)

Answer: B

Solution:

We can use the compound interest formula:

A = P(1 + r/n)^(nt)

Here, P = 100, r = 8% = 0.08, n = 2 (because semiannually), and t = 2. Therefore, we have:

A = 100(1 + 0.08/2)^(2 x 2)

A = 100(1 + 0.04)^4

Answer: B

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