Question

The difference in SI and CI on a certain sum of money in $ 2 $ years at $ 15\% $ p.a. is Rs. $ 144 $ . The sum is
A. $ $ Rs. $ 6000 $
B. Rs. $ 6200 $
C. Rs. $ 6300 $
D. Rs. $ 6400 $

Answer 1

Hint: Here SI stands for Simple interest and CI stands for the interest. Interest is the amount one has to pay for using someone else’s money. In compound interest, interest is calculated for the interest incurred in the previous year. Here sum is the principal value and to get its value we will place the given data in the formula and simplify for the required value.

Complete step-by-step answer:
We can calculate the sum by using the formula,
Sum $ = (SI - CI) \times {\left( {\dfrac{1}{R}} \right)^T} $
Place the given values in the above expression –
Sum $ = (144) \times {\left( {\dfrac{{100}}{{15}}} \right)^2} $
Simplify the above expression –
Sum $ = (144) \times \left( {\dfrac{{100}}{{15}}} \right) \times \left( {\dfrac{{100}}{{15}}} \right) $
Common factors from the numerator and the denominator cancels each other.
Sum $ = 6400 $ Rs.
Hence, from the given multiple choices the option D is the correct answer.
So, the correct answer is “Option D”.

Note: Remember the difference between simple interest and compound interest and apply its concept accordingly and wisely. Compound interest can be well defined as the interest paid for the interest earned in the previous year along with the current year.