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Compound Interest

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by manik11 » Sat Feb 20, 2016 8:51 am
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!
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Source: — Data Sufficiency |

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by [email protected] » Sat Feb 20, 2016 9:36 am
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

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Rich
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by manik11 » Sat Feb 20, 2016 9:50 am
[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
Thanks a lot Rich! I realize my mistake now.
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by Brent@GMATPrepNow » Sat Feb 20, 2016 11:24 am
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
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by manik11 » Sat Feb 20, 2016 11:30 am
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
Brent, this question is from the Bell curves free practice set.
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