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CI Question

by MI3 » Sun Jun 19, 2011 7:05 am
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

Unfortunately, I don't know the answer to this problem. Experts please advise IMO answer should be A
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by Frankenstein » Sun Jun 19, 2011 7:19 am
Hi,
1st month: Amount = 1000(1+0.1) = 1100
He pays x. So, the balance after 1st month is 1100-x
2nd month: Amount = (1100-x)(1.1)
He pays x. So, the balance after 1st month is (1100-x)1.1 -x
3rd month: Amount = [(1100-x)1.1 -x](1.1)
He pays x and balance should be zero.
So, [(1100-x)1.1 -x](1.1) = x => 1331 = 3.31x
So, x = 402.1


Another Method:
If the installment value is x after 1 month, then it contributes to x/1.1 to the current value
Similarly, installment value is x after 2 month, then it contributes to x/(1.1)^2 to the current value
Similarly, installment value is x after 1 month, then it contributes to x/(1.1)^3 to the current value
So, total current value = x/1.1 + x/(1.1)^2 + x/(1.1)^3 = 1000
Solving, we get x = 402.

Hence, C
Cheers!

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by GMATGuruNY » Sun Jun 19, 2011 11:23 am
MI3 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

Unfortunately, I don't know the answer to this problem. Experts please advise IMO answer should be A
We can plug in the answers, which represent the amount paid each month.

Answer choice C: 402 ≈ 400.
Interest charged for first month = .1(1000) = 100.
Total after payment = 1000+100-400 = 700.
Interest charged second month = .1*700 = 70.
Total after payment = 700+70-400 = 370.
Interest charged third month = .1*370 = 37.
Total after payment = 370+37-400 = 7.
Since $7 is left, the monthly payment must be just a bit more than 400; thus, answer choice C is correct.

The correct answer is C.
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by edvhou812 » Sun Jun 19, 2011 5:30 pm
You need to remember that interest is charged. Also need to remember that the interest is compounded monthly.

First month: 1000*1.1 = 1,100. 1,100/3 = About $366
Second month: 1100-366 = 734; 734*1.1 = About 807; 807/2 = about $403
Third month. 807-403 = 404; 404*1.1 = About 444 (Final payment)

366+403+444= $1213. 1213/3 = About 404. We did a bit of rounding above, so the answer must be 402. Answer: C
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by Frankenstein » Sun Jun 19, 2011 8:41 pm
edvhou812 wrote:You need to remember that interest is charged. Also need to remember that the interest is compounded monthly.

First month: 1000*1.1 = 1,100. 1,100/3 = About $366
Second month: 1100-366 = 734; 734*1.1 = About 807; 807/2 = about $403
Third month. 807-403 = 404; 404*1.1 = About 444 (Final payment)

366+403+444= $1213. 1213/3 = About 404. We did a bit of rounding above, so the answer must be 402. Answer: C
Hi,
This is simply not correct. If you had any other option which is closer to 404, you would have chosen that?
Cheers!

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by amit2k9 » Sun Jun 19, 2011 10:05 pm
hmm liked the first method here.
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