Question

Karina borrowed ₹ $ 50,000 $ from Karishma at simple interest of $ 12\% $ per annum for $ 2 $ years and Ankur lent the same amount to Vidya on the same day at $ 12\% $ per annum compound interest for $ 2 $ years. Find Ankur’s gain after $ 2 $ years.

Answer 1

Hint: To find difference of amount or Ankur’s gain on ₹ $ 50,000 $ for $ 2 $ years we first calculate simple interest on a given amount and then we find compound interest on the same amount. Then we find the difference of the amount so obtained to get the required solution of the problem.
Formals used: Simple Interest (S.I.) = $ \dfrac{{P \times R \times T}}{{100}} $ , where P is the principle or amount borrowed, R is the rate and T is the time for which amount is borrowed.
Amount in case of compound interest (C.I.) = $ P{\left( {1 + \dfrac{R}{{100}}} \right)^t},\,\,C.I. = A - P, $ , where P is the principle or amount borrowed, R is the rate and T is the time for which amount is borrowed.

Complete step-by-step answer:
Karina borrowed ₹ $ 50,000 $ form Karishma at simple interest.
Therefore, Principle \[ = \]₹ $ 50,000 $
 $ R = 12\% $
 $ T = 2\;years $
Simple interest (S.I) $ = \dfrac{{P \times R \times T}}{{100}} $
Substituting values of $ P,\,\,R\,\,and\,\,T $ in the above simple interest formula. We have,
Simple interest (S.I) $ = \dfrac{{50,000 \times 12 \times 2}}{{100}} $
Simple interest (S.I) $ = $ ₹. $ 12,000 $
Therefore, we see that Simple interest on the amount ₹ $ 50,000 $ is ₹. $ 12,000 $ .
Now, we will calculate the amount for the same principle but for compound interest.
P = ₹. $ 50,000 $
R = $ 12\% $ and
T = $ 2\;years $
 $ Amount = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $
Substituting values of P, R and T in above formula to obtain value of Amount.
 $ \therefore $ Amount $ = 50,000{\left( {1 + \dfrac{{12}}{{100}}} \right)^2} $
 $ \Rightarrow $ Amount $ = 50,000{\left( {\dfrac{1}{1} + \dfrac{3}{{25}}} \right)^2} $
 $ \Rightarrow $ Amount $ = 50,000{\left( {\dfrac{{25 + 3}}{{25}}} \right)^2} $
 $ \Rightarrow $ Amount $ = 50,000 \times {\left( {\dfrac{{28}}{{25}}} \right)^2} $
 $ \Rightarrow $ Amount $ = 50,000 \times \dfrac{{28}}{{25}} \times \dfrac{{28}}{{25}} $
 $ \Rightarrow $ Amount $ = 5 \times 100 \times 100 \times \dfrac{{28}}{{25}} \times \dfrac{{28}}{{25}} $
 $ \Rightarrow $ Amount $ = 5 \times 4 \times 4 \times 28 \times 28 $
Amount = ₹ $ 62,720 $
Now, to find compound interest we find the difference of the amount calculated above and principle given.
 $ \therefore $ C.I = Amount - Principle
 $ C.I = $ $ 62720 - 50,000 $
 $ C.I = $ ₹ $ 12,720 $
From above we see that difference of compound interest (C.I.) and simple interest (S.I.) is ₹ $ 12,720 $ - ₹. $ 12,000 $
= ₹. $ 720 $
Hence, from above we see that Ankur’s gain is ₹. $ 720 $ more than that of Karishma.
So, the correct answer is “ ₹. $ 720 $ ”.

Note: In case of simple interest or compound interest problems students must consider two factors carefully before solving the problem. One is that rate must be in per annum if time is in year and in the second case if time is not in years then it must be converting into years as rate is in years. For months we divide it by $ 12 $ and for days we divide it by $ 365\,\,or\,\,366 $ if it is mentioned as a leap year.