Question

The simple interest on a certain sum for 3 years is ₹225 and the compound interest on the same sum at the same rate for 2 years is ₹153. Find the rate of interest and the principal.

Answer 1

S.I = P×R×T/100

=> 22500= P×R×3

=> PR = 22500/3 or 7500

=> P = 7500/R ------(i)

C.I = P(1+R/100)^n

=> 153 = P((100+R)/100)^2

=> 153 = P((100)² + 200R + R²))/10000

=> 1530000 = 10000P + 200PR + R²

=> 1530000 = 10000×7500/R + 200×7500/R×R + R²

=> 1530000 = 75000000/R + 150000 + R²

=> 1530000 = (75000000+150000R)/R + R²

=> 1530000 = R²(75000000+150000R) + R / R³

=> 1530000 = R(R(75000000+150000R) + 1)/R³

=> 1530000 = R(75000000+150000R) / R²

=> 1530000R = 75000000 + 150000R

=> 1380000R = 75000000

=> R = 75000000/1380000

=> R = 7500/138

=> R = 54.34 %

P = 7500/54.34

P = Rs. 138.01