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

Question

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:

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$250

Correct Answer:  $250

vyassaptarashi · Accepted Answer

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

gurpreetsingh · Answer

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

firang · Answer

wow, that's a tough solution, is there an easier way to do this?.... anyone.

gurpreetsingh · Answer

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.

Nayimoni · Answer

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.

nonameee · Answer

Is this type of questions tested on the GMAT?

fluke · Answer

YES.

CI and SI are important.

KarishmaB · Answer

Please check my signature for the link to the relevant blog posts.

nonameee · Answer

Karishma, the answer to the problem at the end of the article is 1/9 ?

nonameee · Answer

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.

KarishmaB · Answer

Yes. Or in % terms, you can say that it is 11.11% since rate of interest is generally quoted in %.

KarishmaB · Answer

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/

nonameee · Answer

Karishma, thanks a lot. I will take a look at it now.

alphonsa · Answer

Is this a 700 level question?

Bunuel · Answer

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.

siddharthasthana · Answer

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

adityasuresh · Answer

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:

Show Spoiler

$250

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

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