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If a loan of P dollars, at an interest rate of r percent

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by gmattesttaker2 » Sun Jun 08, 2014 8:39 pm
Hello,

I am not able to solve this question. Can you please assist?

If a loan of P dollars, at an interest rate of r percent per year compounded monthly, is payable in n monthly installments of m dollars each, then m is determined by the formula:

m = (rP/1200)/( 1 - (1 + r/1200)^-n)

John and Sue took out loans whose monthly installments were determined by using the formula above. Both loans had the same interest rate and the same number of monthly installments. John's monthly installment was what percent of Sue's monthly installment?

(1) The amount of Sue's loan was 4 times the amount of John's loan.

(2) Sue's monthly installment was 4 times John's monthly installment.

OA: D


The compound interest formula that I use from MGMAT guide is

CI = P (1 + r/n)^(nt)

where, r = annual rate of interest, n = number of times a year and t = number of years.


I was not sure if for this question, I first needed to simplify the formula given in the question since monthly installment is n.

Thanks a lot for your help,
Sri
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by manyaabroadtpr » Mon Jun 09, 2014 12:06 am
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by GMATGuruNY » Mon Jun 09, 2014 1:47 am
The formula is irrelevant.
It is offered for one purpose only: to induce us to do unnecessary work.
The problem can be rephrased as follows:
John and Sue each took out a loan. Both loans had the same annual interest rate, payable in the same number of monthly installments. John's monthly installment was what percent of Sue's monthly installment?

(1) The amount of Sue's loan was 4 times the amount of John's loan.

(2) Sue's monthly installment was 4 times John's monthly installment.
Statement 1: The amount of Sue's loan was 4 times the amount of John's loan.
Since Sue's loan is 4 times John's loan, her monthly installment is 4 times John's monthly installment.
Thus, for every $1 John pays monthly, Sue pays $4 monthly, implying that J/S = 1/4 = 25%.
SUFFICIENT.

Statement 2: Sue's monthly installment was 4 times John's monthly installment.
Thus, for every $1 John pays monthly, Sue pays $4 monthly, implying that J/S = 1/4 = 25%.
SUFFICIENT.

The correct answer is D.
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by matlab » Fri Oct 02, 2015 2:50 am
in This case, I am interested in finding n? ln?
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