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Hi

I'm completely familiar with this type of question, but this one really confused me.
I think I have a problem with the question. why do you assume she pays end of each month of the loan. I've thought she will give for 3 months and then she will repay for 3 months equally.

I've read all of the Pm blow the post, but I didn't get the answer...

can someone help plz?
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Re: Louie takes out a three-month loan of $1000. The lender [#permalink] ### Show Tags 1 sachinrelan wrote: Louie takes out a three-month loan of$1000. The lender charges him 10% interest per month compunded 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 ≈ 402

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Re: Louie takes out a three-month loan of $1000. The lender [#permalink] ### Show Tags ScottTargetTestPrep wrote: sachinrelan wrote: Louie takes out a three-month loan of$1000. The lender charges him 10% interest per month compunded 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 ≈ 402

nice explanation
now I can understand where I went wrong

thanks to you man Manager  B
Joined: 07 Jun 2018
Posts: 104
Louie takes out a three-month loan of $1000. The lender [#permalink] ### Show Tags 1 After almost 2 days of floundering over this, the ultimate antidote has emerged. Bumpy texts ahead, so get your paper and pencil/pen and let's ride together. The question asks us to find to the monthly payment on a$1000 loan at 10% monthly interest compounded monthly for three months. Let's define the variables:
P= principal = $1000.00 i= monthly interest rate = 10% = 0.1 c= compound growth rate = 1 + I = 1.1 x= monthly payment (to be calculated) At the start, Louie's outstanding balance is P. During the next month, the balance grows by a factor of c as it accumulates interest, then decreases by x when Louie makes his monthly payment. Therefore, the balance after Month-1 is Pc-x. Each month, you must multiply the previous balance by c to accumulate the interest, and then subtract x to account for Louie's monthly payment. In chart form: Balance at start: P Balance after Month-1: Pc-x Balance after Month-2: [Pc-x]c-x=x(c+1) Balance after Month-3: [Pc^2-x(c+1)]c-x=Pc^3-x(c^2+c+1) Finally, the loan should be paid after the third month, so the last loan balance must equal 0. Therefore: Pc^3 - x(c^2+c+1)=0 x(c^2+c+1)=Pc^3 x= (Pc^3)/(c^2+c+1) Note that c=1.1 c^2=1.21 c^3=1.331 So, x=1000(1.331)/(1. 21+1.1+1) x=1331/3.31 x=402 Of course, you won't do this while taking your exam. Just get the understanding, then go back to Page 1 and get some shortcuts. Intern  B Joined: 13 Jan 2016 Posts: 8 Re: Louie takes out a three-month loan of$1000. The lender  [#permalink]

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Bunuel wrote:
sachinrelan wrote:
Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compunded 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 Couldn't solve by a systematic approach. 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. Bunuel How would we change this statement I mean what difference in the statement would be if we had to collect compound interest for 3 month which is 1331 and then divide it by 3 installements ? I mean please make a question statement where 1331/3 so we can notice the difference in both statement and don't get confused. Board of Directors D Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 5033 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: Louie takes out a three-month loan of$1000. The lender  [#permalink]

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1
sachinrelan wrote:
Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compunded 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 $$Amount = 1000( 1 + 10/100)^3$$ Amount is 1331 Since repayment is to be made in 3 equal installments , EMI is 1331/3 = 433 , Answer must be (D) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) SVP  D Joined: 24 Nov 2016 Posts: 1723 Location: United States Re: Louie takes out a three-month loan of$1000. The lender  [#permalink]

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sachinrelan wrote:
Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compunded 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 loan repaid per month: 1000/3 = 333 first 10% 1000 = 100 second 10% 1000-333 = 67 third 10% 1000-333-333 = 33 total interest owed: 200/3 = 67 equal payments per month: 333+67=~400 Answer (C). Intern  B Joined: 17 Jun 2019 Posts: 31 Location: Israel Concentration: Technology, Leadership GPA: 3.95 WE: Engineering (Computer Hardware) Re: Louie takes out a three-month loan of$1000. The lender  [#permalink]

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what a loan shark but nice question. too bad it is just multiplying numbers and nothing more
Intern  B
Joined: 22 Jul 2018
Posts: 29
Re: Louie takes out a three-month loan of $1000. The lender [#permalink] ### Show Tags Abhishek009 wrote: sachinrelan wrote: Louie takes out a three-month loan of$1000. The lender charges him 10% interest per month compunded 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

$$Amount = 1000( 1 + 10/100)^3$$

Amount is 1331

Since repayment is to be made in 3 equal installments , EMI is 1331/3 = 433 , Answer must be (D)

Why option D is not the answer?
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Posts: 10797
Location: Pune, India
Re: Louie takes out a three-month loan of $1000. The lender [#permalink] ### Show Tags Montyyy95 wrote: Abhishek009 wrote: sachinrelan wrote: Louie takes out a three-month loan of$1000. The lender charges him 10% interest per month compunded 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

$$Amount = 1000( 1 + 10/100)^3$$

Amount is 1331

Since repayment is to be made in 3 equal installments , EMI is 1331/3 = 433 , Answer must be (D)

Why option D is not the answer?

The solution will be as given by Bunuel in the comment on first page.

Why not this? Interest is always calculated on the outstanding amount only. If I pay say $400 at the end of month 1 out of the$1100 (P + I) till then, my interest in the second month will be charged on $700 only. This calculation assumes no payment till month 3 to get the amount of$1331. That is not correct.
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Karishma
Veritas Prep GMAT Instructor Re: Louie takes out a three-month loan of $1000. The lender [#permalink] 27 May 2020, 01:32 Go to page Previous 1 2 3 [ 50 posts ] # Louie takes out a three-month loan of$1000. The lender  