stevetaylor wrote:
I saw this problem on
Magoosh and was curious if it is actually solvable:
At the beginning of January 2003, Jill invested money in an account that collected interest, compounding monthly. Assume the annual percentage rate of interest remained constant. What is the total amount she has invested after seven years?
Statement #1: her initial investment was $15,000
Statement #2: In April, 2004, she earned $38.93 in interest
The answer is (C) and I understand the logic that we are only missing one variable (the interest rate) so we should be able to solve, but I can't quite work it out how it is actually solved; can someone please advise?
Cheers!
Dear Steve,
I'm happy to respond! This is Mike McGarry, the author of this very question.
Part of my respond is that asking how to solve for the numerical answer of a DS is, as I believe you understand, profoundly irrelevant to solving the question. That's the first very important point: for a DS question as such, the actual route to the numerical answer is strictly irrelevant.
Now, putting that aside, suppose this were a PS question and we had to solve, or at least estimate. How would we do that? Well, keep in mind that, even though this is a perfectly valid DS of an appropriate difficulty level, if we transform this into a PS, it becomes much much harder than the GMAT would ask. Let's modify it slightly:
At the beginning of January 2003, Jill invested $15,000 in an account that collected interest, compounding monthly. Assume the annual percentage rate of interest remained constant. In April, 2004, she earned $38.93 in interest. Approximately what is the annual interest rate?
(A) 1.5%
(B) 3.0%
(C) 6%
(D) 7.5%
(E) 12% Even that is a beast, a very difficult GMAT question.
Here's a blog you may find helpful:
Compound Interest on the GMATLet's say that the annual interest rate, expressed as a decimal, is R. Then each month, the amount in the count is increased by the percent represented by R/12. Thus, the multiplier would be (1 + R/12), the multiplier for a R/12 percent increase. Thus, the amount after M months would be
\(A = (15000)*(1 + \frac{R}{12})^M\)
To do an exact calculation with that formula would require a calculator. Here's how we might approach an approximation.
In the very first month, the interest earned is exactly R/12 percent of the starting amount, 15,000. With each successive month, the interest piles up, and the amount is slightly more than R/12 percent of 15,000. I'm going to to some fast and loose approximation.
Jill made $38.93 in her 16th month of earning interest, and this is slightly more than what she earned in her first month. Let's say she earned exactly $36 in her first month. Well, $36 is what percent of 15000? Expressed as a decimal, we can simply divide
\(\frac{36}{15000} = \frac{12}{5000} = \frac{24}{10000} = 0.0024\)
That's the estimate percent in the first month. Multiply that by 12 for the annual percent: round the fraction up to 0.025, which is easier to multiply by 12. We know 12 x 25 = 300, so for
12 x 0.025, we get an estimate of 0.03, or 3%. That's a very rough approximation, but since the answer choices were spread out, as they most likely would be in an official question, we can easily select the answer,
(B) for the PS question.
Does all this make sense?
Mike
Great explanation Mike !! But i think its 12 * 0.0025 and not 12 * 0.025 !!