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, here is the step by step solution:

Step 1: Understand the problem The problem is about compound interest (CI). We are given that the interest rate is 20% per annum, the time period is 2 years, and the difference in the amount of interest when it is compounded yearly and half-yearly is Rs 482. We need to find the principal amount.

Step 2: Use the formula for compound interest 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.

Step 3: Set up the equation We know that the difference in the amount of interest when it is compounded yearly and half-yearly is Rs 482. So, we can set up the equation as follows: P(1 + r)^(t) - P(1 + r/2)^(2t) = 482

Step 4: Substitute the given values into the equation Substitute r = 20/100 = 0.2 (convert the percentage to a decimal), t = 2 into the equation: P(1 + 0.2)^(2) - P(1 + 0.2/2)^(2*2) = 482 Solving this equation will give us the value of P.

Step 5: Solve the equation This is a quadratic equation in P. You can solve it by factoring, completing the square, or using the quadratic formula. The solution will give you the principal amount.