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Louie takes out a three-month loan of $1000. The lender charges him 10

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Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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New post 15 Nov 2011, 14:28
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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

Again can someone please explain the concept behind solving these problems? Unfortunately, I again don't have an answer for this question.

OPEN DISCUSSION OF THIS QUESTION IS HERE: louie-takes-out-a-three-month-loan-of-1000-the-lender-101506.html
[Reveal] Spoiler: OA

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Re: Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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New post 15 Nov 2011, 14:47
(See alternate explanation in the follow up post).

Please verify that you typed the answer choices (or the question) correctly.

Since there's a 10% interested compound every month (meaning you pay interest on the principal amount plus the interest on interest):

After 1st month, amount owed is 1000+10%(1000) = 1100.
After 2nd month, 1100+10%(1100) = 1210
After 3rd month, 1210+10%(1210) = 1331

Since total amount owed is $1331 and it must be done in 3 equal payments, each payment comes to $1331/3 = $443.7 (which is none of the options).

Last edited by kostyan5 on 15 Nov 2011, 15:09, edited 1 time in total.
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Re: Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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New post 15 Nov 2011, 14:54
Thanks kostyan5. Even I got the same answer as your's. So I think the answer choices are incorrect. Many thanks for the help.
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Re: Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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New post 15 Nov 2011, 15:08
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Actually what I wrote above assumes that Louie doesn't start repaying the loan immediately, instead he waits until all the interest has compounded. This is not necessarily correct since usually you start paying off loans as soon as you take them out. This means that you pay off some principle each month and therefore your interest is lower.

Here's the calculation for that case, assume monthly payment is X.

After 1st month: (1000)(1.1)-X = 1100-X
After 2nd month: (1100-X)(1.1)-X = 1210-2.21X
After 3rd month: (1210-2.21X)(1.1)-X = 1331-3.31X

Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:

1331-3.31X = 0
X = 1331/3.31 = 402.11

The answer is C. However, I think this is a poorly worded question and on the real GMAT, they would specify that the payment is to be started immediately after loan inception.
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Re: Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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New post 16 Nov 2011, 02:18
Very absorbing article. Very interesting and well written post. I will come back in the near future.
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Re: Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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New post 16 Nov 2011, 15:16
Hi Kostyan - Ok here is my understanding of your solution. When you say let's monthly payment be x.

So A=P(1+r/100)^n ----------------------------------------------------------------(1)

A= 1000(1+0.1)^1 = 1100.

So Principle for 2nd month will be 1100-x -------------------------------------(Am I right over here?)

Again using the same formula as 1

A = (1100-x) (1+0.1)^1 = 1210-1.1x ---------------> How did you get 1210-2.21x?

So Principle for the 3rd month will be 1210-1.1x-x = 1210-2.1x----------------------(Am I right over here?)

A = (1210-2.1x) (1+0.1)^1 = 1331 - 2.31x

Amount after the last payment should be Zero. Therefore,

1331 - 2.31x = 0 => 2.31x=1331 => x=
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Re: Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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New post 16 Nov 2011, 19:54
You're right. Principle for 3rd month should be 1210-2.1x. I made a type, but the rest of the calculations were unaffected.

Keep in mind that you still need to make 3rd payment in month 3. So 1331 - 2.31x-x =0 or 1331-3.31x=0.
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Re: Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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Re: Louie takes out a three-month loan of $1000. The lender charges him 10 [#permalink]

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New post 07 May 2016, 04:20
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enigma123 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

Again can someone please explain the concept behind solving these problems? Unfortunately, I again don't have an answer for this question.


Let the monthly payment be \(x\).

After the 1st month there will be \(1,000*1.1-x\) dollars left to repay;
After the 2nd month there will be \((1,000*1.1-x)*1.1-x=1,210-2.1x\) dollars left to repay;
After the 3rd month there should be 0 dollars left to repay: \((1,210-2.1x)*1.1-x=0\) --> \(1331=3.31x\) --> \(x\approx{402}\)

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: louie-takes-out-a-three-month-loan-of-1000-the-lender-101506.html
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Re: Louie takes out a three-month loan of $1000. The lender charges him 10   [#permalink] 07 May 2016, 04:20
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