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23 Apr 2010, 09:29
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Question Stats:

54% (05:43) correct 46% (05:42) wrong based on 43 sessions

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The interest compounded annually on a certain sum of money is $41.60 after two years. The simple interest on the same amount of money after two years would be$40.00. Find the amount invested if the interest rate would be the same in each investment.

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05 May 2011, 13:03
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3
I can give u the easiest solution
This question requires the basic understanding of SI and CI and their relation

Compound interest is the interest accrued on the previous interest value.
But at the end of one year CI is equal to SI

Now, the second year SI = 40 and CI = 41.6 ... therefore 41.6 - 40 = 1.6 is the interest that is accrued on the previous years interest.

Now, since SI at the end of second year is 40 and SI of the each year is the same, therefore we can say that SI at the end of the first year = 20

Thus 1.6 is the interest accrued on the first years interest i.e. 20
therefore, rate of interest = 1.6/20 * 100 = 8%

Thus, now we can find Principle
We know that PNR/100 = SI therefore P*2*8 /100 = 40
Hence P = 250
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink] Show Tags 23 Apr 2010, 09:58 gmatt14 wrote: Hi all. The interest compounded annually on a certain sum of money is$41.60 after two years. The simple interest on the same amount of money after two years would be $40.00. Find the amount invested if the interest rate would be the same in each investment. Correct Answer:$250

Can anybody suggest a step-by-step approach?

Suppose interest rate is x% .....take $$\frac{x}{100} = y$$

now for Compound interest
Amount = $$P(1+\frac{x}{100})^2 = P(1+y)^2$$
Interest = Amount - principal = $$P*(1+y)^2-P = P*(1+y^2+2y-1)$$ = $$P*y^2 + 2Py = 41.6$$ -----------1

Now Simple interest = $$P*\frac{x}{100} *2 = 2Py = 40$$------------------------2

Now subtract 2nd equation from 1
you will get $$P*y^2 = 1.6$$ ------------3
since $$2Py=40 => Py=20$$ and $$P^2*Y^2 = 20*20$$----------4

Divide 4 by 3 you will get P = 250
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28 Apr 2010, 07:44
firang wrote:
wow, that's a tough solution, is there an easier way to do this?.... anyone.

Its not complicated, just to explain the question nicely steps are increased.

Just do one thing, follow the answer explanation and do it side by side on the paper.
It will be easy to understand why those steps were performed.
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink] Show Tags 05 May 2011, 12:28 Let X be the investment amount and x the interest rate We have x ( (1+x/100)^2 - 1) = 41.6 for the compound investment and 2 * X * x/100 =40 for the simple interest Replace x/100 by 20/X in the compound equation to get: (20 + X)^2 / X - X = 41.6, so (20+X)^2 - X^2= 41.6 X. Distribute and simplify to get 1.6 X = 400 so X equals 4000/16 or 250$

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19 Sep 2011, 02:01
nonameee wrote:
Is this type of questions tested on the GMAT?

YES.

CI and SI are important.
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19 Sep 2011, 03:09
Karishma, the answer to the problem at the end of the article is 1/9 ?
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19 Sep 2011, 03:35
nonameee wrote:
Karishma, the answer to the problem at the end of the article is 1/9 ?

Yes. Or in % terms, you can say that it is 11.11% since rate of interest is generally quoted in %.
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19 Sep 2011, 03:59
Karishma, thanks a lot. I will take a look at it now.
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05 Nov 2014, 09:06
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alphonsa wrote:
Is this a 700 level question?

Personally, I would not rate this question as 700, though the statistics on similar question HERE say it is in fact 700 level.

Check other Compound Interest Problems in our Special Questions Directory.

Hope it helps.
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink] Show Tags 31 May 2019, 08:40 bumpbot wrote: Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. For 1st year, both CI and SI will be equal-->20. For 2nd year, difference between CI and SI occurs bcz 20$ from 1st year will also earn interest in case of CI.
1.60=20xRx1/100--> R=8%
For principal amount--> 20=Px8x1/100
P=250