Question

The simple interest on certain sum for 3 years is rupees 225 and the compound interest on the sum at the same rate for 2 years is Rs 153 find the rate of interest and principal

Answer 1

Simple interest for 3 years = 225

=> Simple interest for each year = 225/3 = 75

Now, SI = CI = 75 for 1st year.

In second year, CI is Rs 3/- more than SI. It is due to interest on interest of Rs 75 for first year.

=> Rate of Interest = 3/75 x 100 = 4% p.a.

Now, Rs 75 interest for first year is 4% of principal.

=> Principal = 75/(4%) = 75 x 100/4

= Rs 1875

Check :

P = 1875

SI = prt/100 = 1875 x 4 x 2/100 = 150

CI :

A = P(1 + r/100)^2

= 1875(1 + 0.04)^2

= 2028

CI = A - P = 2028 - 1875 = 153