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22 Sep 2010, 09:39
1
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Difficulty:

95% (hard)

Question Stats:

32% (01:38) correct 68% (01:50) wrong based on 1573 sessions

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 [Reveal] Spoiler: OA Kudos [?]: 166 [1], given: 7 Math Expert Joined: 02 Sep 2009 Posts: 41872 Kudos [?]: 128639 [15], given: 12181 Re: Compound Interest - Lender Charges [#permalink] ### Show Tags 22 Sep 2010, 09:53 15 This post received KUDOS Expert's post 30 This post was BOOKMARKED 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: $$(1,210-2.1x)*1.1-x=0$$ --> $$1331=3.31x$$ --> $$x\approx{402}$$

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Re: Compound Interest - Lender Charges [#permalink]

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22 Sep 2010, 09:47
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sachinrelan wrote:

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06 Feb 2013, 03:05
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Why are we assuming he pays from the 3rd month? The question does not specify that, it just says he has to pay in 3 installments.

Why not this way?
Total Loan disbursed in 3 months = 1.1 * 1.1* 1.1* 1000 = 1331
Repaid in 3 months, hence per month = 1331/3 = 443
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Re: Compound Interest - Lender Charges [#permalink]

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22 Sep 2010, 11:13
1
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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. This is the same method i have used to solve the question, but can you suggest some short cut to solve this ques as i felt this approach in the exam would take lot of time to solve !! Kudos [?]: 166 [1], given: 7 Intern Joined: 18 Jun 2012 Posts: 38 Kudos [?]: 9 [1], given: 15 Louie takes out a three-month loan of$1000. The lender [#permalink]

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07 Jul 2012, 05:15
1
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The interest has to be calculated on a reducing balance.
If monthly repayment = x
At the end of the 3 month period,
1.1*[1.1*{1.1*(1000)-x}-x]-x = 0
=> 3.31x = 1331
=> x ~ 402

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21 Apr 2013, 04:15
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Expert's post
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atalpanditgmat wrote:
Bunuel, Can you give links to similar problem? It would be great help. Thanks

Check here: search.php?search_id=tag&tag_id=191

Hope it helps.
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Re: Compound Interest - Lender Charges [#permalink]

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02 Feb 2014, 09:17
1
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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. It's so frustrating to get to the 3.31x = 1331 and then get the answer wrong. I did heavy division shortcut but still the answer choices are a bit close. Any suggestion other than long division to better approximate this division? Cheers J Kudos [?]: 719 [1], given: 355 Manager Joined: 23 Sep 2013 Posts: 105 Kudos [?]: 26 [1], given: 80 Concentration: Strategy, Marketing WE: Engineering (Computer Software) Re: Louie takes out a three-month loan of$1000. The lender [#permalink]

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04 Sep 2014, 08:02
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A slightly easier approach.

As we know compound interest is slightly greater than the simple interest calculated for the same period.

So instead calculate SI for this period.
Rate per month is 10%. Therefore rate per annum is 12*10 = 120%
Simple interest to be paid at the end = 1000* (120/100)= 1200

Simple Interest to be paid each month of 3 month pay back period =1200/3= 400

Now since Compound interest is slightly greater than Simple interest i.e. answer is 402.

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Re: Compound Interest - Lender Charges [#permalink]

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22 Sep 2010, 11:20
shaselai 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. ok, there is an interest formula that i forget but lets do it another way: so basically he is getting 10% interest per month for TWO month since he pays off in 3 months. so 1000*1.1*1.1 = 1210 now divide by 3 = ~403.333 C I Couldnt get why interest would be paid for 2 months, as per me 1. 1st month at the end monthly interest would be Accrued and monthly installment would be deducted from that amount. 2. For 2nd month start amount would be remaining amt of 1st month and at the end of 2nd month, monthly interest would be Accrued and thereafter again monthly installment would be deducted 3. For the 3rd month start amt would again be the remaning amt of 2nd month and at the end of 3rd month monthly interest would be accrued which should be equal to monthly installment. So as per this interest was paid thrice ..request you to please clarify !! Kudos [?]: 166 [0], given: 7 Current Student Status: What's your raashee? Joined: 12 Jun 2009 Posts: 1837 Kudos [?]: 273 [0], given: 52 Location: United States (NC) Concentration: Strategy, Finance Schools: UNC (Kenan-Flagler) - Class of 2013 GMAT 1: 720 Q49 V39 WE: Programming (Computer Software) Re: Compound Interest - Lender Charges [#permalink] ### Show Tags 22 Sep 2010, 11:27 sachinrelan wrote: shaselai 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.

ok, there is an interest formula that i forget but lets do it another way:
so basically he is getting 10% interest per month for TWO month since he pays off in 3 months.
so 1000*1.1*1.1 = 1210
now divide by 3 = ~403.333
C

I Couldnt get why interest would be paid for 2 months, as per me

1. 1st month at the end monthly interest would be Accrued and monthly installment would be deducted from that amount.
2. For 2nd month start amount would be remaining amt of 1st month and at the end of 2nd month, monthly interest would be Accrued and thereafter again monthly installment would be deducted
3. For the 3rd month start amt would again be the remaning amt of 2nd month and at the end of 3rd month monthly interest would be accrued which should be equal to monthly installment.

So as per this interest was paid thrice ..request you to please clarify !!

this is because you are paying off in the third and last months. This is assuming the interest rate is calculated at the end of the month. So it is assumed you paid off the balance at the end of third month so 0 balance. Like CC statements - if you didnt pay off your statement by end of month you get charged interest - you dont get charged interest throughout.
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09 Feb 2013, 18:43
why its not 443 (1331/3)

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21 Apr 2013, 01:02
Bunuel, Can you give links to similar problem? It would be great help. Thanks
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24 May 2013, 08:18
1000 * 1.1 = 1100 month one plus compounded interest
1100 - 402 = 698 first months payment @ "correct" answer
698 * 1.1 = 767.80 month 2 balance plus interest
767.80 - 402 = 365.80 payment deducted for month two
365.8 * 1.1 = 402.38

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Re: Compound Interest - Lender Charges [#permalink]

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11 Sep 2013, 03:59
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. I get a different answer by using the Compound Interest formula, i.e- P[1 +(r)/100n]^nt Since this formula uses annualized figures, so: r = 10% per month = 120% per year n = 12 (as interest is compounded monthly) t = 3 months = 3/12 years Using the formula for compound interest, I get: P + C.I = 1000(1.1)^3 = 1331 So, EMI = 1331/3 = 443.66 which is ~$444

What's wrong with this approach?

Thanks,
Ishan

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Re: Compound Interest - Lender Charges   [#permalink] 11 Sep 2013, 03:59

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