Louie takes out a three-month loan of $1000. The lender

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

Louie takes out a three-month loan of $1000. The lender

by Vincen » Tue Feb 13, 2018 3:56 am

Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?

A)333
B)383
C)402
D)433
E)483

The OA is the option C.

This is an interesting question, but I don't know what are the formulas that I should use. Experts, may you give me some help? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Tue Feb 13, 2018 3:56 am

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Feb 14, 2018 10:12 am

Vincen wrote:Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?

A)333
B)383
C)402
D)433
E)483

We can let p be his monthly payment.

At the end of the first month, the loan will accrue 0.1(1000) = 100 dollars of interest, and the total amount is $1100. Since he will pay p dollars to that amount, he has 1100 - p dollars left to pay.

At the end of the second month, the loan will accrue 0.1(1100 - p) dollars of interest, and the total amount is 1.1(1100 - p) dollars. Since he will pay p dollars to that amount, he has 1.1(1100 - p) - p = 1210 - 2.1p dollars left to pay.

At the end of the third month, the loan will accrue 0.1(1210 - 2.1p) dollars of interest, and the total amount is 1.1(1210 - 2.1p) dollars. Since he will pay p dollars to that amount, he has 1.1(1210 - 2.1p) - p = 1331 - 3.31p dollars left to pay. However, since we assume that he will pay off this loan in 3 months, it must be true that what he has left to pay is $0. That is,

1331 - 3.31p = 0

1331 = 3.31p

p = 1331/3.31 â‰ˆ 402

Answer: C

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