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

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

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

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.

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.

Is this type of questions tested on the GMAT?

YES.

CI and SI are important.

Please check my signature for the link to the relevant blog posts.
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Karishma, the answer to the problem at the end of the article is 1/9 ?

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.

Yes. Or in % terms, you can say that it is 11.11% since rate of interest is generally quoted in %.
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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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Karishma, thanks a lot. I will take a look at it now.

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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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

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