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

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

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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

Source: Beat The GMAT — Problem Solving | Thu Nov 19, 2020 11:24 am

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

by Scott@TargetTestPrep » Wed Nov 25, 2020 8:30 am

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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