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compound interest

by yeshuashley » Fri Sep 26, 2014 9:41 am
Saw this problem in an article on Beat the GMAT but would somebody please explain how to solve this problem? Thank you!

Michelle deposited a certain sum of money in a savings account on July 1st, 2012. She earns an 8% annual interest compounded semi-annually. The sum of money in the account on January 1st, 2015 will be approximately what percent of the initial deposit?

(A) 117%

(B) 120%

(C) 121%

(D) 135%

(E) 140%
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by [email protected] » Fri Sep 26, 2014 10:35 am
Hi yeshuashley,

This is an interest rate question; based on it's wording, it requires the use of the compound interest formula (although you could calculate the interest every 6 months "by hand", but that would take a bit of work).

In most GMAT questions of this type, interest is calculated once per year, with the following formula:

Total = (Principal)(1 + R)^T

Principal = the initial money invested
R = Interest Rate per year
T = Number of years

So if you invested $100 at 10% compound interest for 2 years, you'd have....

($100)(1 + .1)^2
($100)(1.21)
$121 at the end of the two years.

In this question, we're calculating interest semi-annually, which means we calculate every 6 MONTHS. This changes the calculation a bit. Since we're calculating interest twice a year, we have to essentially "double the T and halve the R." This question includes one more "quirk" - the period of time is NOT in full years - it's five 6-month periods. This leads us to....

Principal = $X
R = 4%
T = 5 periods

We can TEST VALUES by picking a number for the Principal:

($100)(1.04)^5

This would be a real tedious calculation IF we didn't have the answers to work with. Since we're receiving 4% interest per period, and there are 5 periods, we know that 4%(5 periods) = 20%.....but since we're compounding the interest, the total would be a little bit more than 20%. There's only one answer here that accounts for the initial Principal and interest that is a little more than 20%.

Final Answer: C

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by GMATGuruNY » Fri Sep 26, 2014 10:53 am
yeshuashley wrote:Saw this problem in an article on Beat the GMAT but would somebody please explain how to solve this problem? Thank you!

Michelle deposited a certain sum of money in a savings account on July 1st, 2012. She earns an 8% annual interest compounded semi-annually. The sum of money in the account on January 1st, 2015 will be approximately what percent of the initial deposit?

(A) 117%

(B) 120%

(C) 121%

(D) 135%

(E) 140%
On the GMAT:
compound interest = (simple interest) + (a little more).

Let the original investment = 100.

8% interest compounded semi-annually means that 4% is earned every 6 months.
On $100, 4% simple interest = $4.
From July 2012 to January 2015 = five 6-month intervals.
If $4 simple interest is earned during each of these five 6-month intervals, the resulting amount in January 2015 = 100 + 5*4 = $120.
Since the actual interest is compounded, the resulting amount in January 2015 must be just a bit more than $120.
Thus, the resulting amount in January 2015 must be just a bit more than 120% of the original investment.

The correct answer is C.
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