A sum of money is put on CI for 2 years at 20%. It would fetch Rs 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.

Sure, let's solve this step by step.

1. First, let's understand the concept of Compound Interest (CI). When interest is compounded annually, the interest is added to the principal at the end of each year. But when it is compounded half-yearly, the interest is added to the principal twice a year.

2. Given that the rate of interest is 20% per annum. So, for half-yearly compounding, the rate would be 20/2 = 10% for every 6 months.

3. Let's assume the principal amount (the sum of money put on CI) to be P.

4. The formula for compound interest is A = P(1 + r/n)^(nt), where: A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (in decimal). n is the number of times that interest is compounded per year. t is the time the money is invested for in years.

5. If the interest is compounded annually, the amount after 2 years would be A1 = P(1 + 20/100)^2.

6. If the interest is compounded half-yearly, the amount after 2 years would be A2 = P(1 + 10/100)^(2*2).

7. It is given that A2 is Rs 482 more than A1. So, we can write the equation as: P(1 + 10/100)^(2*2) - P(1 + 20/100)^2 = 482.

8. Solving this equation will give us the value of P, which is the sum of money put on CI.

Please note that this is a quadratic equation and you might need to use the quadratic formula or factoring to solve it.