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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]
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]
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]
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]
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]
nonameee wrote:
Is this type of questions tested on the GMAT?


YES.

CI and SI are important.
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The interest compounded annually on a certain sum of money is $41.60 a [#permalink]
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Please check my signature for the link to the relevant blog posts.

Originally posted by KarishmaB on 19 Sep 2011, 02:52.
Last edited by KarishmaB on 11 Oct 2022, 00:46, edited 1 time in total.
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]
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]
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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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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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: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/02 ... rcentages/
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]
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]
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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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 $41.60 a [#permalink]
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For 1st year, both CI and SI will be equal-->20.
For 2nd year, difference between CI and SI occurs bcz 20$ 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
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Re: The interest compounded annually on a certain sum of money is $41.60 a [#permalink]
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.

Compound interest and simple interest will be the same for year 1
$41.6 - $40 = $1.6 = Difference between CI & SI in year 2
Simple interest for 2 years = $40. Per year SI = $20
Let Rate = R
$1.6 = \(R/100\) * 20 (Interest on interest will be the same as interest on principle)
R = 8
Now calculate SI Principle is the unknown, SI for 2 years = $40, R = 8% N =2
Substituting \(P*N*R/100\) = Simple interest
=\(P*2*8/100\) = 40
P = \(40*100/2*8\) = $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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