Question

Compound Interest compounded quarterly on Rs. 15000 for 3 years is Rs. 986 more than

Simple Interest on the same principal for 3 years. Find the rate of interest​

Answer 1

Rate of interest = 12%

Step-by-step explanation:

Principal - 15000

quarterly interest = r/100 * 3/12 = r/400

SI = 15000 * 12 * r/400 = 450r

CI = 15000 ( 1 + r/ 400) ^ 12 - 15000

Given CI = SI + 986

15000 ( 1 + r/ 400) ^ 12 - 15000 = 450r + 986

15000 ( 1 + r/ 400) ^ 12  - 450r = 15986

(1 + r/400)^12 = 450r/15000 + 15986/15000

(1 + r/400)^12 - 0.03r = 1.0657 -------------(1)

Substituting various values of r in the equation (1) to find the closest value:

Assuming r = 5%

(1 + 5/400)^12 - 0.03 * 5 = 1.011

Assuming r = 10%

(1 + 10/400)^12 - 0.03 * 10 = 1.0449

Assuming r = 12%

(1 + 12/400)^12 - 0.03 * 12 = 1.0657 --------------(2)

Equation 2 matches equation 1.

So rate of interest = 12%