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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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17
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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
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 59265

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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 _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings Gmat test review : http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html Intern  Joined: 12 Oct 2009 Posts: 20 Location: I see you Re: The interest compounded annually on a certain sum of money is$41.60 a  [#permalink]

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wow, that's a tough solution, is there an easier way to do this?.... anyone.
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GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 ### Show Tags

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$Hope this is helpful. _________________ http://www.hannibalprep.com Director  Joined: 23 Apr 2010 Posts: 504 Re: The interest compounded annually on a certain sum of money is$41.60 a  [#permalink]

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Is this type of questions tested on the GMAT?
Retired Moderator Joined: 20 Dec 2010
Posts: 1557

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To read up some theory of simple and compound interest, check out: http://www.veritasprep.com/blog/2011/03 ... imple-one/
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Karishma
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Director  Joined: 23 Apr 2010
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And one more:

In your computations you work with fractions rather than with decimal numbers. Is there some trick to it or do you simply convert decimals to fractions in your head?

Thanks.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9803
Location: Pune, India

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nonameee wrote:
And one more:

In your computations you work with fractions rather than with decimal numbers. Is there some trick to it or do you simply convert decimals to fractions in your head?

Thanks.

Yeah, I almost never work with decimals. I might just convert my answer to decimal form at the end. Working with fractions will almost always cut down the amount of work you will need to do. It's far more intuitive when you start using it regularly. Most decimals that you come across can be converted to fractions in your head e.g. 0.01 = 1/100, 4.5 is half of 9 so 9/2 etc
I do remember some conversions e.g.
1/8 = 12.5% or .125
1/9 = 11.11% or .1111
1/11 = 9.09% or .0909
1/6 = 16.66% or .1666
etc
Check out this post for some commonly used fraction-decimal-percent conversions: http://www.veritasprep.com/blog/2011/02 ... rcentages/
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Karishma
Veritas Prep GMAT Instructor

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Is this a 700 level question?
Intern  B
Joined: 04 May 2014
Posts: 11
Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink] ### Show Tags bumpbot wrote: Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. For 1st year, both CI and SI will be equal-->20. For 2nd year, difference between CI and SI occurs bcz 20$ 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 Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink] 31 May 2019, 08:40 Display posts from previous: Sort by # The interest compounded annually on a certain sum of money is$41.60 a  