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The interest compounded annually on a certain sum of money is $41.60 a

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The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 23 Apr 2010, 09:29
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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.

Correct Answer:
$250

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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 05 May 2011, 13:03
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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
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 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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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 28 Apr 2010, 07:30
wow, that's a tough solution, is there an easier way to do this?.... anyone.
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 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]

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New post 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$

Hope this is helpful.
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 19 Sep 2011, 01:49
Is this type of questions tested on the GMAT?
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 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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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 19 Sep 2011, 02:52
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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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 19 Sep 2011, 03:09
Karishma, the answer to the problem at the end of the article is 1/9 ?
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 19 Sep 2011, 03:11
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.
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 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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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 19 Sep 2011, 03:42
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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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 19 Sep 2011, 03:59
Karishma, thanks a lot. I will take a look at it now.
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 05 Nov 2014, 08:56
Is this a 700 level question?
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]

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New post 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]

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Re: The interest compounded annually on a certain sum of money is $41.60 a   [#permalink] 04 Mar 2018, 06:26
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