If $4,000 is invested at 12% annual interest compounded every 4 months, what will be the total value, to the nearest cent, of the investment at the end of a year?
A) $4,502.04
B) $4,499.46
C) $4,484.46
D) $4,480.00
E) $4,370.90
OA : B
Hi Experts...For this question I had setup the compound interest formula as follow:
Maturity amount = 4000(1 + 12/4%) ^4. This gave me 4000(1.03)^4 and the math got very ugly. Eventually I had to guess and move on. Could you please tell if there is a smarter and more efficient way to handle such compound interest problems?
Thanks!
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Compound Interest
This topic has expert replies
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi manik11,
To start, you made an error in your translation - the prompt states that interest is compounded EVERY 4 MONTHS - so at the 4th month, at the 8th month and at the 12th month. That's 3 'periods' (not 4). So your equation should actually be...
Maturity amount = 4000(1 + 12/3%)^3.
That having been said, you might find it easier to perform each calculation individually (as opposed to trying to do one gigantic calculation).
From the prompt, we know that there will be 3 calculations and each will be 4% of the total....
1st = $4,000(1.04) = $4,000 + $160 = $4160
The next calculation will be slightly higher...
2nd = $4,160(1.04) = $4160 + $166.40 = $4326.40
And the final calculation will be slightly higher than that...
3rd = $4326.40(1.04) = $4326.40 + close to $173 = about $4499
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
To start, you made an error in your translation - the prompt states that interest is compounded EVERY 4 MONTHS - so at the 4th month, at the 8th month and at the 12th month. That's 3 'periods' (not 4). So your equation should actually be...
Maturity amount = 4000(1 + 12/3%)^3.
That having been said, you might find it easier to perform each calculation individually (as opposed to trying to do one gigantic calculation).
From the prompt, we know that there will be 3 calculations and each will be 4% of the total....
1st = $4,000(1.04) = $4,000 + $160 = $4160
The next calculation will be slightly higher...
2nd = $4,160(1.04) = $4160 + $166.40 = $4326.40
And the final calculation will be slightly higher than that...
3rd = $4326.40(1.04) = $4326.40 + close to $173 = about $4499
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
Thanks a lot Rich! I realize my mistake now.[email protected] wrote:Hi manik11,
To start, you made an error in your translation - the prompt states that interest is compounded EVERY 4 MONTHS - so at the 4th month, at the 8th month and at the 12th month. That's 3 'periods' (not 4). So your equation should actually be...
Maturity amount = 4000(1 + 12/3%)^3.
That having been said, you might find it easier to perform each calculation individually (as opposed to trying to do one gigantic calculation).
From the prompt, we know that there will be 3 calculations and each will be 4% of the total....
1st = $4,000(1.04) = $4,000 + $160 = $4160
The next calculation will be slightly higher...
2nd = $4,160(1.04) = $4160 + $166.40 = $4326.40
And the final calculation will be slightly higher than that...
3rd = $4326.40(1.04) = $4326.40 + close to $173 = about $4499
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
This question doesn't seem very GMAT-like. What's the source?
I ask because the answer choices are so close together that one is forced to perform tedious calculations, and the GMAT is not designed to identify human calculators. I wrote an article about this: https://www.gmatprepnow.com/articles/re ... st-maker-0
Cheers,
Brent
I ask because the answer choices are so close together that one is forced to perform tedious calculations, and the GMAT is not designed to identify human calculators. I wrote an article about this: https://www.gmatprepnow.com/articles/re ... st-maker-0
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Brent, this question is from the Bell curves free practice set.Brent@GMATPrepNow wrote:This question doesn't seem very GMAT-like. What's the source?
I ask because the answer choices are so close together that one is forced to perform tedious calculations, and the GMAT is not designed to identify human calculators. I wrote an article about this: https://www.gmatprepnow.com/articles/re ... st-maker-0
Cheers,
Brent
