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Compound interest problem

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by sl750 » Fri Aug 05, 2011 6:34 am
$1200 is invested at a given interest rate for two years. The difference between the simple 2-year non-compounded return at the end of the two years and an annually compounded return is $132. What is the interest rate?

A 10%
B 11%
C 12%
D 13%
E 14%

I understood that I have to form an equation that involves using both simple and compound interest. What I didn't understand was why the period of 2 years was not included in the S.I calculation. Any help is really appreciated

The equation goes as follows
[spoiler]
1200R^2 -1200R = 132[/spoiler]
Doesn't the simple interest formula include the period as well? [ Investment*period*R%]
Answer is A
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by knight247 » Fri Aug 05, 2011 9:54 am
Principal=1200

Simple interest=Principal*Number of yrs*R
=1200*2*R
=4800R

Total accrued amount is 1200+4800R....(1)

Compounded

Total accrued amt=1200(1+R)²
=1200(1+2R+R²)
=1200+4800R+1200R².....(2)

from the problem we have (2)-(1)=132
132=1200+4800R+1200R²-1200-4800R
132=1200R²
R²=132/1200
or
R²=1320000/1200
=13200/12=1100
R=√1100=33%(approximately) None of the answer choices match
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by gmatboost » Fri Aug 05, 2011 10:50 am
Hi,

You've got the right idea and the right answer. You made a few arithmetic mistakes along the way but they happened to cancel out:
Simple interest=Principal*Number of yrs*R
=1200*2*R
=4800R
Simple interest is actually 2400R
Compounded
Total accrued amt=1200(1+R)²
=1200(1+2R+R²)
=1200+4800R+1200R²
This should be 1200 + 2400R + 1200R^2

For compound interest, the interest earned is 1200 + 2400R + 1200R^2 - 1200, since we started with 1200.

So compound interest = 2400R + 1200R^2

So, 2400R + 1200R^2 - 2400R = 132
So, 1200R^2 = 132
R^2 = 132/1200 = 11/100 = 0.11

I suspect the question writer intended this to be the answer. The actual answer, as you said, is the square root of this, which is not a nice round number and is not a choice.
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by sl750 » Sun Aug 07, 2011 12:38 pm
Actually, the answer choice is given as A. However, think the answer explanation provided by the source was faulty to begin with. Thanks though for clearing that up
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by goalevan » Sun Aug 07, 2011 1:51 pm
1,200(1 + r)^2 = 1,200(1 + 2r) + 132
1,200(1 + r)^2 - 1,200(1 + 2r) = 132
1,200[(1 + r)^2 - (1 + 2r)] = 132
1,200[(r^2 + 2r + 1) - (1 + 2r)] = 132
1,200*r^2 = 132
r^2 = 132/1200
r^2 = (2^2 * 3 * 11) / (2^2 * 3 * 2^2 * 5^2)
r^2 = 11/100

r = sqrt(11)/10

B
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