Question

The difference between the compound interest and simple interest on a certain sum at 15% per annum for 3 years is Rs 283.50. Find the sum.

Answer 1

Given: 
CI - SI = Rs 283 . 50
R = 15 % 
n = 3 years
Let the sum be Rs x.
We know that: 
\[A = P(1 + \frac{R}{100} )^n \]
\[ = P(1 + \frac{R}{100} )^n \]
\[ = x(1 + \frac{15}{100} )^3 \]
\[ = x \left( 1 . 15 \right)^3 . . . (1)\]
Also, 
\[SI = \frac{PRT}{100} = \frac{x(15)(3)}{100} = 0 . 45 x\]
\[A = SI + P = 1 . 45x . . . (2)\]
Thus, we have: 
\[x \left( 1 . 15 \right)^3 - 1 . 45x = 283 . 50 \][From (1) and (2)]
\[1 . 523x - 1 . 45x = 283 . 50\]
\[0 . 070875x = 283 . 50\]
\[x = \frac{283 . 50}{0 . 070875}\]
\[ = 4, 000\]
Thus, the sum is Rs 4, 000.