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Carl is facing very difficult financial times and can

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by BTGmoderatorDC » Mon Feb 26, 2018 3:11 pm
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

I'm confused how to set up the formulas here. Can any experts help?

OA C
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Source: — Problem Solving |

by [email protected] » Mon Feb 26, 2018 3:26 pm
Hi lheiannie07,

We're told that Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken, and the bank charges him a quarterly compound rate of 5%. We're asked for the APPROXIMATE interest he pays annually. To start, this question is poorly-phrased. The 'intent' is that the Annual Interest is 20%, compounded quarterly - and that Carl won't make any interest payment until the END of the year. While there is a longer, step-heavy way to calculate the exact amount of interest that will occur over the course of a year, there's a great 'concept shortcut' that you can use to avoid a lot of that math - and still get the correct answer.

For the 1st quarter of the year, the 5% interest on $10,000 would be (.05)($10,000) = $500

With each additional quarter that passes though, there will be 'interest on top of interest', so the interest for the second quarter will NOT be $500 exactly (it will be a little more than $500 - since we're now paying 5% on the extra $500 from the 1st quarter):

For the 2nd quarter of the year, the 5% interest on $10,500 would be (.05)($10,500) = $525

At this point, you don't really need to do any more work to determine the interest at the end of the 3rd and 4th quarters. You know that it will be a bit more than $525 each time, so the OVERALL total for the year will be a bit more than $2,000. There's only one answer that matches...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Wed Feb 28, 2018 10:31 am
lheiannie07 wrote: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
The total amount he has to pay back in a year is:

10,000(1 + 0.05)^4 = $12,155.06

Subtract the principal ($10,000) from this amount; he has to pay $2,155.06 in interest, which is approximately $2,150.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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