A mobile phone is available for $39000 cash or $17000 as dow

Question

A mobile phone is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be

A: 18%

B: 19%

C: 21.2%

D: 21.81%

E: 22.07%

Source: CMAT Preparation

mikemcgarry · Answer

Dear PareshGmat , I'm happy to respond :-)

but I have a few criticisms of this question. I am not familiar with this particular source. First of all, GMAT questions all are scrupulously realistic in terms of the numbers they use in a problem. Perhaps if the currency were something other than US dollars, these numbers would be plausible, but the idea of a mobile phone that costs $39,000 is not realistic in the least -- most automobiles cost less than that! That's one aspect that is not GMAT like. Also, NOBODY walks around with $39,000 in cash on them. That would be wads and wads of bills. Second, the answers are very close together --- if the answers were spread out, we could use estimation, which the GMAT often would employ in a problem of this sort. See: https://magoosh.com/gmat/2012/the-power- ... mat-quant/ In order to get the exact answer here, presumably one would need a calculator or have to do tedious long division --- this is another aspect that is quite unlike the GMAT. Finally, in my calculation, I get an answer very different from the answers here. Under the installment plan, we pay 5*(4800) = 24,000 plus $17,000 for a total of $41,000. That means, we pay $2000 more under the installment plan than we would have paid up front in cash. I understand the question to ask --- the extra $2000 would be what percent of interest on the original $39,000 cost? That would be 2000/39,000 *100% = 2/39 * 100% Well, 2/40 = 1/20 = 0.05 = 5%. If we make the denominator smaller, the whole fraction gets bigger. Thus, 2/39 should be slightly larger than 5% Indeed, a calculator gives 2/39 = 5.1282051282 ...% None of the answer choices are in this range. Something is funny here. Mike :-)

interviewbay22 · Answer

Hi

Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years

the way I see it: on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000

For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)

thus, SI = 2000 or

2000 = (P*R*T)/100
 2000 = (22,000*R*5)/(100*12)

R = (2,000*12*100)/22,000*5
 R = 21.81%

Therefore answer is D

mikemcgarry · Answer

Dear interviewbay22 , My friend, you are using that formula incorrectly ---- I'm not convinced it's really the correct formula for anything meaningful. See this post for simple & compound interest: https://magoosh.com/gmat/2014/compound-i ... -the-gmat/ Among other things, R is an annual interest rate, so we can't have T, time, in months ! More to the point, simple interest means --- quite simply, $2000 is what percent of $22,000? That number is clearly not anything around 20%. One of the major problems with this problem is that the nature of the percentage is not specified in an unambiguously manner. This is an exceptionally poorly written question. Mike :-)

rakshithbabu · Answer

I think the ask in this particular question is just the extra amount paid (interest) will be simple interest of the principle if it were under the simple interest plan for five months.

UJs · Answer

I would skip this question .. :evil:

I agree with Mike, Question not worth spending time on tedious calculation :cry:

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A mobile phone is available for $39000 cash or $17000 as dow

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