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Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

A. 360
B. 390
C. 400
D. 410
E. 420

The OA is C

Source: GMAT Prep

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nathan

by GMATGuruNY » Fri Feb 22, 2019 11:13 am
swerve wrote:Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

A. 360
B. 390
C. 400
D. 410
E. 420
Since the 10% rate is compounded annually, the amount of interest increases by 10% each year:
First-year interest = 10% of 1200 = 120.
Second-year interest = (first-year interest) + 10% = 120 + 12 = 132.
Third-year interest = (second-year interest) + 10% = 132 + 13.2 = 145.2.
Total interest = 120 + 132 + 145.2 = 397.2.

The correct answer is C.
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by Scott@TargetTestPrep » Sun Feb 24, 2019 5:38 am
swerve wrote:Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.

A. 360
B. 390
C. 400
D. 410
E. 420

The OA is C

Source: GMAT Prep
We can use the annual compound interest formula: A = P(1 + r)^t. So we have:

A = 1200(1 + 0.1)^3

A = 1200(1.1)^3

A = 1597.2

The amount of $1597.20 is the total amount (principal plus interest) he owes, so the amount of interest he owes is 1597.2 - 1200 = $397.2, or approximately $400.

Answer: C

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