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

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

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New post 23 Oct 2017, 09:19
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]

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New post 14 Feb 2018, 10:59
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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


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

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

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New post 15 Feb 2018, 02:56
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

Answer: C


nice explanation
now I can understand where I went wrong

thanks to you man
:cool:
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Louie takes out a three-month loan of $1000. The lender  [#permalink]

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New post 02 Aug 2018, 05:51
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.
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Re: Louie takes out a three-month loan of $1000. The lender  [#permalink]

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New post 07 Aug 2018, 23:25
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.
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Re: Louie takes out a three-month loan of $1000. The lender  [#permalink]

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New post 08 Aug 2018, 07:58
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)
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Re: Louie takes out a three-month loan of $1000. The lender &nbs [#permalink] 08 Aug 2018, 07:58

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