Question

The simple interest on a certain sum for 3 years in Rs. 225 and the compound interest on the same sum for 2 years is Rs. 165. Find the rate percent per annum.

Answer 1

Given:

(i) The simple interest on a certain sum for 3 years in Rs. 225 and the compound interest on the same sum for 2 years is Rs. 165.

To find:

(i) The rate of interest per annum.

Solution:

We know that the Simple Interest value in each year remains the same.

Given, the SI for 3 years is Rs 225.

So, SI for 1st year is = Rs (225/3) = Rs 75

SI for 2 years = Rs (75*2) = Rs 150.

We know that SI and CI of the first year are equal.

So, CI of 1st year = Rs 75.

CI of 2nd year = Rs (165-75) = Rs 90.

CI - SI (of 2 years) = Rs (165-150) = Rs 15

Let the rate of interest be r% p.a.

r% of 75 = 15

⇒ 75r/100 = 15

⇒ r = 1500/75

⇒ r = 20

Rate = 20% p.a.

The rate of interest is 20% p.a.