To calculate the compounded interest on Rs. 5000 for 2(1/2) years at an annual interest rate of 5%, compounded half-yearly, we can follow these steps:
1. First, let's determine the number of compounding periods in 2(1/2) years. Since interest is compounded half-yearly, there will be 2 compounding periods per year. Therefore, in 2(1/2) years, there will be a total of 5 compounding periods (2 x 2 + 1 = 5).
2. Next, we need to calculate the interest for each compounding period. The formula to calculate compound interest is given by: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the total number of years.
3. In this case, the principal amount (P) is Rs. 5000, the annual interest rate (r) is 5% (or 0.05 as a decimal), the number of compounding periods per year (n) is 2, and the total number of years (t) is 2(1/2) = 2.5 years.
4. Plugging these values into the compound interest formula, we get:
A = 5000(1 + 0.05/2)^(2 x 2.5)
A = 5000(1.025)^(5)
A ≈ 5000(1.1314084)
5. Calculating the final amount, we have:
A ≈ 5657.04
6. Finally, to find the compounded interest, we subtract the principal amount from the final amount:
Compounded Interest = A - P
Compounded Interest = 5657.04 - 5000
Compounded Interest ≈ 657.04
Therefore, the compounded interest on Rs. 5000 for 2(1/2) years at an annual interest rate of 5%, compounded half-yearly, is approximately Rs. 657.04.