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22 Sep 2010, 09:39
3
KUDOS
30
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

31% (02:42) correct 69% (01:55) wrong based on 1139 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 Math Expert Joined: 02 Sep 2009 Posts: 32652 Followers: 5655 Kudos [?]: 68710 [9] , given: 9818 Re: Compound Interest - Lender Charges [#permalink] ### Show Tags 22 Sep 2010, 09:53 9 This post received KUDOS Expert's post 13 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
7
KUDOS
1
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. 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 _________________ If you like my answers please +1 kudos! Senior Manager Joined: 20 Jul 2010 Posts: 269 Followers: 2 Kudos [?]: 61 [2] , given: 9 Re: Compound Interest - Lender Charges [#permalink] ### Show Tags 22 Sep 2010, 10:29 2 This post received KUDOS $$CI = P(1+\frac{r}{100})^t$$ Assume he pays off entire amount in 3rd month or interest is accrued for 2 months. Find the amount at end of 3 months and divide by 3 to know monthly EMI _________________ If you like my post, consider giving me some KUDOS !!!!! Like you I need them Intern Joined: 27 Jun 2010 Posts: 40 Followers: 0 Kudos [?]: 97 [1] , given: 7 Re: Compound Interest - Lender Charges [#permalink] ### Show Tags 22 Sep 2010, 11:13 1 This post received KUDOS 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: $$(1,210-2.1x)*1.1-x=0$$ --> $$1331=3.31x$$ --> $$x\approx{402}$$

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 !!
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06 Feb 2013, 03:05
1
KUDOS
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: Louie takes out a three-month loan of $1000. The lender [#permalink] ### Show Tags 21 Apr 2013, 04:15 1 This post received KUDOS Expert's post 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. _________________ Current Student Joined: 06 Sep 2013 Posts: 2035 Concentration: Finance GMAT 1: 770 Q0 V Followers: 43 Kudos [?]: 456 [1] , given: 355 Re: Compound Interest - Lender Charges [#permalink] ### Show Tags 02 Feb 2014, 09:17 1 This post received KUDOS 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: $$(1,210-2.1x)*1.1-x=0$$ --> $$1331=3.31x$$ --> $$x\approx{402}$$

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
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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 !! Current Student Status: What's your raashee? Joined: 12 Jun 2009 Posts: 1847 Location: United States (NC) Concentration: Strategy, Finance Schools: UNC (Kenan-Flagler) - Class of 2013 GMAT 1: 720 Q49 V39 WE: Programming (Computer Software) Followers: 22 Kudos [?]: 228 [0], given: 52 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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20 Apr 2013, 23:28
summer101 wrote:
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

Because he pays each month. He doesn't have to pay interest on the amount that he has already paid.

IE. If he is paying $402 a month, then at the end of the first month his balance will be (1000 * 1.1) - 402 =$698, so going into the second month that 10% interest is only accruing on $698 rather than on the full$1000.
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23 Apr 2013, 01:00
rajatr wrote:
In case of CI ,Repayment in equal installments (X) can be given as:

X =P*r/ [1-(100/100+r)^n]

where X :each installment
r: rate
n: number of installments
P: Principal amount borrowed by borrower.

So in this case it would be 1000*10/[1-(10/11)^3] = 133100/331 = 402

P(1+R/100)^n

Can we do this using this formula?
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Re: Louie takes out a three-month loan of $1000. The lender [#permalink] ### Show Tags 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 Intern Joined: 01 Feb 2013 Posts: 12 Location: India Followers: 0 Kudos [?]: 6 [0], given: 4 Re: Compound Interest - Lender Charges [#permalink] ### Show Tags 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: $$(1,210-2.1x)*1.1-x=0$$ --> $$1331=3.31x$$ --> $$x\approx{402}$$

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 Math Expert Joined: 02 Sep 2009 Posts: 32652 Followers: 5655 Kudos [?]: 68710 [0], given: 9818 Re: Compound Interest - Lender Charges [#permalink] ### Show Tags 11 Sep 2013, 05:29 Expert's post ishanbhat455 wrote: 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: $$(1,210-2.1x)*1.1-x=0$$ --> $$1331=3.31x$$ --> $$x\approx{402}$$

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 ~ $444 What's wrong with this approach? Thanks, Ishan Since he pays after each month, then after the firs month (after the first payment) the interest is calculated on reduced balance. Does this make sense? _________________ Re: Compound Interest - Lender Charges [#permalink] 11 Sep 2013, 05:29 Go to page 1 2 Next [ 35 posts ] Similar topics Replies Last post Similar Topics: 1 Nathan took out a student loan for 1200$ at 10 percent annual interest 1 22 Dec 2015, 21:18
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