GRE Interest Problems
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Interesting Interest
Deposit money into a savings account and you will earn interest. Rack up a bunch of charges on your credit card, and you’re going to be charged interest. In the real world, the bank takes care of calculating interest for you, but if the word “interest” shows up on the GRE, you’re going to need to know how to calculate it yourself.
Simple Interest
Simple interest is just that. Simple. Take that percent of the principal and tack it on.
Alice invested $1000 at 8% simple annual interest. How much is the investment worth after one year?
Some terms you should know:
The principal: The amount originally deposited. With a debt, it’s the amount you borrowed initially.
The interest rate: Usually “annual,” the interest rate is the percentage of the principal earned over a period of time.
Calculate 8% of that $1000 principal. (8/100 * 1000 = 80). Over the year Alice earned $80, so at the end of the year, the account is worth $1080. Done.
You could use your calculator, too (though it may be a waste of time). Convert the interest rate into a decimal (.08) and add 1 (1.08). [That 1 represents the original principal.] Multiply that principal by 1.08.
$1000 x 1.08 = 1080
With simple interest, the percent is always based on the original amount, so for multiple years, Alice will continue to earn $80 every year. Over 5 years, Alice would earn $400 simple interest.
Compound Interest
“Compound interest” means that every so often, the bank will add something to the principal (or the credit card company will add something to your debt). Each time after that, the bank will calculate the next interest payment based on the NEW amount of money in the principal. Over a short amount of time, compounding will add only a smidge to the principal. Over a long period of time, compounding can add a great deal to the principal (as I learned the hard way after college).
Every so often you’ll see confusing statements such as “8% annual interest compounded semi-annually” or “12% annual interest compounded quarterly.”
“8% annual interest compounded semi-annually” means the bank will divide that 8% over the year by the number of “periods” in that year. Semi-annually means twice a year, so the bank will divide that 8% by 2. You get 4% every six months.
“12% annual interest compounded quarterly” means you get 12%/4, or 3% four times a year (every 3 months).
“24% annual interest compounded monthly” mean you get 2% 12 times a year (every month).
Technique 1: Brute Force/Be the Bank
The most effective and efficient way to work out compound interest on the GRE is to pretend to be the bank. Just work each payment out, piece by piece, one “period” at a time. Consider the following question:
Alice invested $1000 at 8% annual interest compounded every 6 months (semi-annually). How much is the investment worth after one year?
Look at the annual interest, and divide it by the number of periods each year. 8% divided by 2 periods a year = 4% every period. Then get to work.
Alice puts $1000 into the account, where it sits for 6 months. After 6 months, Alice is going to get some interest. Since it’s halfway through the year, she’ll get half of that 8%.
4% of $1000 is $40, which will be added to her account. She now has $1040.
At the end of the year, she’ll get the other 4%, but since the interest is compounded, she’ll get 4% of the 1040 that’s in her account now!
4% of 1040 is 41.60, which will be added to her account, leaving her with $1081.60.
Technique 2: Simple Plus a Smidge
Imagine the same question, but it’s multiple choice this time:
Alice invested $1000 at 8% annual interest compounded every 6 months (semi-annually). How much is the investment worth after one year?
(A) $1040
(B) $1080
(C) $1081.60
(D) $1160
(E) $1166.40
If you know that “compounding” adds a tiny bit of interest over a short amount of time, you can get THIS one very very quickly.
All you do is figure out the simple interest over the year, and pick the answer that’s a teeny tiny bit more than that.
If it were simple interest, 8% annual interest would be $80, leaving $1080 in the account. But since the interest is compounded, the only possible answer is the one a tiny bit more than that: (C) 1081.60.
Technique 3: The Compound Interest Formula
But what if the answers look funny?
Amy invested $5000 at 12% annual interest compounded quarterly. How much is her investment worth after 5 years?
This is one of the few cases in which it’s important to know the “compound interest formula.” The Official Guide to the GRE gives us a formula that is nearly incomprehensible and very easy to get messed up:
What? Huh? Forget it.
Let’s break this down and make this MUCH easier. Ask yourself a few questions:
What’s the interest rate every period? Convert that to a decimal.
How many periods? How many times is money going into the account?
In Amy’s case, “12% annual interest compounded quarterly” means she’s getting 12/4, or 3% every period. As a decimal, that’s .03.
“Compounded quarterly” over 5 years means she’ll be getting money 4 x 5 = 20 times.
A simplified version of the formula is this, V = value of the investment:
We already figured out that her rate per period is .03, with 20 periods. Therefore, the value of Amy’s investment after 5 years will be 5000(1.03)20. Answer choice (E).
Back to our original problem:
Alice invested $1000 at 8% annual interest compounded every 6 months (semi-annually). How much is the investment worth after one year?
(A) $1040
(B) $1080
(C) $1081.60
(D) $1160
(E) $1166.40
The formula would be 1000(1.04)² = 1081.60.
Keep in mind, the GRE calculator does NOT do exponents, so you’d have to key in 1000 x 1.04 x 1.04, which may be tedious and error-prone.
In Sum
When you get an interest problem on the GRE, ask yourself a few questions:
Is this simple or compound?
If it’s compound, can I ballpark the answer with “Simple plus a smidge?”
If not, would it be better to use brute force (be the bank) or to apply the compound interest formula (if the answers look like the interest formula)?
We have tons of examples in the Manhattan Prep 5-lb Book of GRE Practice Problems, so get to work locking in those skills! ?
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When not onstage telling jokes, Neil Thornton loves teaching you to beat the GRE and GMAT. Since 1991, he’s coached thousands of students through the GRE, GMAT, LSAT, MCAT, and SAT, and trained instructors all over the United States. He scored 780 on the GMAT, a perfect 170Q/170V on the GRE, and a 99th-percentile score on the LSAT. Check out Neil’s upcoming GRE course offerings here or join him for a free online study session twice monthly in Mondays with Neil.