Question

What is the sum if the difference between the compound and simple interest on a certain sum at $ 14\% $ per annum for $ 2 $ years is $ Rs\,100? $
A. $ 3102 $
B. $ 4102 $
C. $ 5102 $
D. $ 6102 $

Answer 1

Hint: In this question we have been given the difference between Compound interest and Simple interest i.e. $ Rs\,100 $ . So we will first find the compound interest and then simple interest . The formula of Compound interest that we will use here is $ C.I = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} - P $ .After this we will calculate the simple interest by the formula $ \dfrac{{P \times R \times T}}{{100}} $ .

Complete step-by-step answer:
In the given question we have rate,
 $ R = 14\% $
Time or number of years:
 $ T = n = 2 $ .
We do not have the principal value i.e. P, so we will leave it as it is.
And the difference i.e.
 $ C.I - S.I = 100 $
By putting the values in the formula, we can calculate compound interest or C.I.
 $ P{\left( {1 + \dfrac{{14}}{{100}}} \right)^2} - P $
We will add the values inside the bracket:
 $ P{\left( {\dfrac{{100 + 14}}{{100}}} \right)^2} - 1 $
 $ P\left( {\dfrac{{114}}{{100}} \times \dfrac{{114}}{{100}}} \right) - P $
On simplifying we have:
 $ P\left( {1.2996 - 1} \right) $
It gives us the value
 $ C.I. = 0.2996P $
Now we will calculate the simple interest ;
 $ \dfrac{{P \times 14 \times 2}}{{100}} $
On simplifying it gives us the value
 $ \dfrac{{28P}}{{100}} = 0.28P $
Now we have been given
  $ C.I. - S.I = 100 $
We will put the values of compound interest and simple interest :
 $ 0.2996P - 0.28P = 100 $
On subtracting, we have:
 $ 0.0196P = 100 \Rightarrow P = \dfrac{{100}}{{0.0196}} $
Further simplifying we have:
 $ P = \dfrac{{100 \times 10000}}{{196}} = Rs\,5102.04 $
Hence the correct option is (C) $ 5102 $ .
So, the correct answer is “Option C”.

Note: We should know that in simple interest the amount on which the interest is levied is constant. We calculate simple interest on the particular rate of interest for a particular period of time. However, in the compound interest, the amount on which the interest is levied is changed after each year by adding the interest gained that year to the total amount.