A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs 482 more, if the interest was payable half-yearly than if it was payable annually. The sum is: (a) Rs 10,000     (b) Rs 20,000    (c) Rs 40,000    (d) Rs 50,000

Explanation

To solve the problem step by step, we need to calculate the compound interest for both half-yearly and annually, and then find the principal amount based on the difference given.

### Step 1: Define the variables
Let the principal amount (the sum of money) be denoted as \( P \).

### Step 2: Calculate the compound interest for half-yearly compounding
For half-yearly compounding, the interest rate is halved and the number of compounding periods is doubled.

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