Carl is facing very difficult financial times and can only pay

Question

Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 5%. What is the approximate interest he pays annually?
(A) $1200
(B) $2000
(C) $2150
(D) $2500
(E) $12000

Source: Optimus Prep

nimitparikh · Answer

An easy way too attempt this is by approximation:

For the first quarter, he pays 5% of 10,000 which is $500.

So for the four quarters in the year, he will approximately play 500*4=2000 over the entire year. Look at the options - A is clearly wrong as it is way below the approximate payment. B is again lower than the actual amount (remember that it would be 2000 if it was simple interest, but since it is compound interest, it is higher then 2000). C seems to be right. D and E are again way higher than the approximated answer.

Hence, it is C.

naeln · Answer

Thank you. I fretted because I couldn't apply the compound interest formula.

EMPOWERgmatRichC · Answer

Hi naeln,

This prompt isn't written in the typical GMAT "style" for these types of questions. Normally, the prompt would state something to the effect that "....the bank charges interest of 20%, compounded quarterly...."

Regardless of the wording, you can still use the compound interest formula....

(Principal)(1 + R)^T

(10,000)(1.05)^4

....but as nimitparikh points out, the answer choices are "spaced out" in such a way that you can use some estimation and a bit of logic to get to the correct answer without doing that much math.

GMAT assassins aren't born, they're made,
Rich

naeln · Answer

Hi Rich,
Thank you for the feedback. I have a question regarding the compound interest formula. Don't we need to divide the 5% by the number of compoundings per year in which case we will have to divide 0.05 by 4 so will have 
10000 (1+ 0.05/4)^4 
Could you please explain why dividing by 4 is not right!!!

KarishmaB · Answer

Usually, you are given the annual rate of interest and it is mentioned that it is annual rate.

"The bank charges him a quarterly compounded ANNUAL rate of 20%."

Here you find per quarter rate as (20/4)% = 5%

I have actually never seen a question with quarter rate given but since this question did not mention "annual rate of interest" and since the options did not make sense with 5% annual rate of interest, it is apparent that the intent was a 5% quarterly rate. So the bank charges 5% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 5% of 10,000 = $2000 as our answer. 
But since, the interest is compounded, it will be a bit more than $2000. Option (C) looks correct.

EMPOWERgmatRichC · Answer

Hi naeln,

If the 5% interest rate was for the YEAR, then you would have to divide that by 4 to calculate the quarterly interest (and multiply the number of 'periods' by 4). The way this prompt was written, the implication is that it's 5% per quarter, compounded quarterly. The example that I included in my original post (annual interest of 20%, compounded quarterly) is the equivalent of that idea.

GMAT assassins aren't born, they're made,
Rich

mvictor · Answer

well.. I believe the question is written poorly, as one might comprehend that the interest is 5%, and the interest for the quarter to be 1.25%.
nevertheless, it can easily be found the answer by using simple interest:
10% = 1,000, and 5% = 500.
4 quarters, thus 500*4 = 2,000$.
since it's a compounded interest, it has to be more than 2,000. we can eliminate A and B.
E can't be, since 12,000 - is even more than 10,000. thus, it is smth above 100%, which can't be.
between C and D - since it is only for 1 year, the interest compounded would not be "much". thus, we can rule out D (because it is more ~5 periods if simple interest), and select C as the answer.

mvictor · Answer

bumping again for review
again..consider this one a poorly written question.
another flaw I found - can pay only the interest..but when does he pay interest? each quarter? or at the end of the year?
if each quarter, then 2000 is the total he pays annually. if at the end of the year, smth slightly more than 2000

ShashankDave · Answer

I need help with the guesstimation approach. I understand every part of this approximation we have done here. I also understand that the final value will be more than 2000, since it is compound interest. My questions is..

How do we know if the final value is closer to 2150 than it is to 2000?

This is the only question that troubles me in this type of problems. Please help.

gracie · Answer

$10,000*1.05^4-$10,000≈$2150 
C

bumpbot · Answer

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Carl is facing very difficult financial times and can only pay

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