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
