Hi, there. I'm happy to give my two cents on this one.
The short answer is: on the GMAT itself, when you don't have a calculator, there is no short way to figure that out. But take heart; the GMAT is simply not going to ask you to calculate something for which you would need a calculator.
One thing the GMAT might expect is for you to estimate
. For example, consider the slightly modified question:John deposits $5000 in a savings account for 5 years. The interest rate is 2.33% compounded annually for 5 years. Estimate the amount he has at the end of five years.
Yes, the formula is the same, but because the problem specifies that we can estimate, and because the answer choices are widely spaced, we don't have to do the exact formula as written. We can use easier numbers.
For example, I'm going to approximate 2.33% as 2%. One percent of $5000 is $50, so 2% of $5000 is $100. It interest would be about $100 in the first year, and a little over $100 in each of the next for years, for a total interest of something a little over $500. That would be total account value of a little over $5500.
Answer (A) is less than the principal, not possible. Answer (B) has far too little interest. Answer (C) is in the right ballpark. Answer (D) is an absurd amount of interest (over 50% increase over 5 years!), and Answer (E) has to be from a fairy tale it's so unrealistic. Therefore the answer is (C)
. Notice, the only actual math we did in solving that was so easy we could do it in our heads. That's the power of estimation.
The take-aways are
(a) yes, you have the correct formula for compound interest --- kudos to you
(b) you will not have to calculate exact value from that formula on the GMAT unless the numbers are very very simple
(c) estimation is a vitally important skill that several GMAT math questions will demand.
Here's a blog I wrote that posted today, about dealing with the lack of a calculator on the GMAT math section. http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/
I hope that's helpful.
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