Rs. 10000 is being compounded at 20% per annum. Calculate the amount after 2 years if rateof interest is charged half yearly.(a) Rs. 10041(b) Rs. 14641(c) Rs. 12000(d) Rs. 13660

To solve this problem, we need to understand that when interest is compounded half yearly, the rate of interest and the time period both get doubled.

Here's the step-by-step solution:

1. Given, Principal (P) = Rs. 10000, Rate of interest (r) = 20% per annum, Time (t) = 2 years.

2. Since the interest is compounded half yearly, the rate of interest will be halved and the time period will be doubled. So, new r = 20/2 = 10% and new t = 2*2 = 4 periods.

3. The formula for compound interest is A = P (1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate of interest, n is the number of times interest applied per time period and t is the time.

4. Substituting the given values in the formula, we get A = 10000 (1 + 10/100)^4.

5. Simplifying it further, A = 10000 * (1.1)^4 = Rs. 14641.

So, the amount after 2 years when the rate of interest is charged half yearly will be Rs. 14641. Hence, the correct option is (b) Rs. 14641.