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.

Correct option is A

Given,

Principal = Rs. 15000

Formula:

SI = PRT/100

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

Solution:

Principal - 15000

Let rate of interest be r%

Quarterly interest = r × 3/12 = r/4 %

SI = (15000 × 3 × r)/100

SI = 450r

CI = 15000 (1 + r/ 400)¹²- 15000

Also, 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)

Assuming r = 12%

=> (1 + 12/400)¹²- 0.03 × 12 = 1.0657

=> 1.0657 = 1.0657      (satisfied)

∴ We can say rate of interest is 12%