The compound interest on a certain sum of money invested at a certain

Question

The compound interest on a certain sum of money invested at a certain rate of interest in the 2nd year and in the 3rd year was $600 and $720 respectively. What was the rate of interest at which the sum of money was invested?

(A) 12.0%
(B) 12.5%
(C) 15.0%
(D) 20.0%
(E) 25.0%

(A) 12.0%
(B) 12.5%
(C) 15.0%
(D) 20.0%
(E) 25.0%

Abhishek009 · Accepted Answer

ROI  =  \frac{720 - 600}{600}*100

So,  ROI  =  \frac{120}{600}*100

Or,  ROI  =  20  %

Thus, the answer must be (D) 20 %

lenric · Answer

Another way (which will lead to the one already posted):

Let x be the initial investment and y the interest rate:

x(1+y)^2 = 600 
 x(1+y)^3 = 720

Thus:
 x(1+y)^2 = 600 
 x(1+y)^2 * (1+y) = 720

600 (1+y) = 720

y = 0,2  
-> *100 -> 20%

pushpitkc · Answer

Given : 
On a given sum of money invested at a certain rate of interest,
Compound interest earned(2nd year) = 600$
Compound interest earned(3rd year) = 720$

Since, he has to include the 600$ earned during the second year,
while doing the calculations of the interest for the 3rd year, the additional compound interest earned = x% of 600.
Additional interest which is  120$ =\frac{x}{100}* 600 => x =\frac{120}{6} = 20

Rate at which the sum was invested(x) = 20(Option D)

arvind910619 · Answer

Hi Abhishek009
 Please explain the formula in detail.
Thanks in advance .

Abhishek009 · Answer

Dear  arvind910619

There is no formula , its the basic concept of Compound Interest which distinguishes Simple Interest from Compound Interest.
 
In compound Interest we calculate interest for the Interest amount as well, whereas in Simple Interest we calculate Interest only on the principal amount.

Example -

SI on a sum of 100 for 3 years @ 20% pa will be -

SI = \frac{100*3*20}{100} = 60

CI on a sum of 100 for 3 years @ 20% pa will be -

Interest for 1st Year is  \frac{100*1*20}{100}  =  20 
Interest for 2nd Year is  20  +  \frac{20*1*20}{100}  =  24 
Interest for 3rd Year is  24  +  \frac{24*1*20}{100}  =  28.8

Here in this question we are given Amount after 3rd Year, which Includes the Principal amount of 2nd Year which is 600 & Interest for 1 year , ie 120...
  
Hope this helps..

pushpitkc · Answer

Concept tested  
The difference in the compound interests between any two consecutive years includes additional interest,
which is nothing but the interest calculated on the compound interest earned in the first of the consecutive
years.

In this problem, the compound interest for the amount is $600 for the second year & the interest calculated
for the third year is $720. The difference in interest is $120, which is the interest earned on $600. We can
calculate the rate of interest as follows -  \frac{120}{600} * 100 = 20%

Therefore, the rate of interest on which the amount was invested is  20%(Option D)

adstudy · Answer

Let x be the principal amount
Let y be the rate of interest.

We also know  Compound Interest = Principal  ^N - Principal

Now using the same formula and details as per the question we get,

600 = x ^2 - x   --- (1) 
 720 = x ^3 - x   --- (2)

Subtracting (1) from (2), we get

120 = x ^3 - x ^2 
 120 = x ^2 (1 + \frac{y}{100} - 1) 
 120 = x ^2 (\frac{y}{100})   --- (3)

Using (1) in (3), we get

120 = 600 (\frac{y}{100}) 
 \frac{1}{5} = \frac{y}{100} 
   y = 20

Hence D

satya2029 · Answer

Let the interest rate is X
{(1+X/100)^3}/{(1+X/100)^2}=720/600
1+X/100=6/5
X=20
D:)
How to get the equations
Principle amount is P and interest is X, after one year principle amount becomes P1
P1=P+P*X/100
P1=P(1+X/100)
P2=P1+P1*X/100
P2=P1(1+X/100)
P2=P(1+X/100)^2
P3=P(1+X/100)^3
(1+X/100)^3 is nothing but interest after 3 years that is 720 in this problem
same way (1+X/100)^2 interest after 2 years-620

RastogiSarthak99 · Answer

Pretty straightforward if you think about it this way:

CI2 and CI3

600 and 720

720 = 600 * (x% of 600)

therefore 120/600 = x%

1/5 = 20%

And D

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