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

Answer: Rate of Interest = 12%

Step-by-step explanation:

Principle amount = Rs. 15,000

Time Period = 3 years, compounded quarterly

Difference in Interest = Rs. 986

Let rate of interest be x

Simple Interest = $\frac{x}{100 * 4} *12 *15000$

= 450x

Compound Interest = $15000 * (1 + \frac{x}{100 * 4} )^12 - 15000$

Given CI = SI + 986

$15000 * (1 + \frac{x}{100 * 4} )^12 - 15000$ = $\frac{x}{100 * 4} *12 *15000$ + 986

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

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

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

Substituting various values of x in the equation:

Assuming x = 5%

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

Assuming x = 10%

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

Assuming x = 12%

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

This is the closet value

So rate of interest = 12%