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Compound interest

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Compound interest

by Fractal » Sat Jul 09, 2011 1:12 am
$5'000 invested for 1 year at a rate of 8% compounded quarterly

= 5'000(1+0.08/4)^4 = 5'412

I understand the formula, but does anybody have a good way to calculate such expressions? Concrete, how do you calculate (1+0.08/4)^4 * 5000 respectively (1.02)^4 * 5000 in a fast way?

Thx,
fractal
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by amit2k9 » Sat Jul 09, 2011 4:57 am
we use pascals triangle approach for amount and CI.

1-- 1
2--1--2--1
3-1--3--3--1
4-1-4--6--4--1
likewise.

for p=1000,r=10% and n=3

A= 1*1000+3*(10/100* 1000) + 3*(10/100*100) + 1* (10/100* 10) = 1331
for CI = 3*(10/100* 1000) + 3*(10/100*100) + 1* (10/100* 10)= 331.

here 10/100*1000 = 100, 10/100*100 = 10 and 10/100*10 = 1. for the 3 years.

Similarly,

5000(1+(1/50))^4 = 1*5000 + 4(1/50*5000) + 6*(1/50*100) + 4(1/50*2) + 1*(1/50*1/25)
thus 5000+ 400+ 12+ decimal values = 5412 (approx).
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by Brent@GMATPrepNow » Sat Jul 09, 2011 5:41 am
Fractal wrote:$5'000 invested for 1 year at a rate of 8% compounded quarterly

= 5'000(1+0.08/4)^4 = 5'412

I understand the formula, but does anybody have a good way to calculate such expressions? Concrete, how do you calculate (1+0.08/4)^4 * 5000 respectively (1.02)^4 * 5000 in a fast way?

Thx,
fractal
Don't worry - on the GMAT, you will not be required to make such calculations. Remember that this is not meant to be a test of your ability to carry out lengthy calculations.

Some compound interest questions will ask you to identify the expression that represents the final amount. For example, the answer choices for your question might look like this:

A) 5000(1.02)^4
B) 5000(1.08)^4
C) 5000(1.02)^8
etc.

Other questions may ask you to evaluate the final amount, but if you are asked to do this, the number of "compoundings" will not exceed 2.

For example, let's say the annual interest rate is 10% and you invest $5000 for 2 years.
Here, one option is to use the formula to get: final amount = 5000(1.1)^2, which you can then calculate to get $6050

Alternatively, you can pretty much do this one in your head if you calculate the interest for each year.

After 1 year, the interest is $500 (10% of 5000 is 500), which means you now have $5500

After another year, the interest is $550 (10% of 5500 is 550), which means you now have $6050

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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