Question

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

Answer 1

Dear Student

Simple interest for 3 years = 225

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

Now, Simple Intrest = Compound Intrest = 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 = p*r*t/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

hope this helps you