Calculation of Present Value of ₹10000 due in 2 years at 5%pa Compound Interest paid Half-Yearly

Step 1: Calculate the Half-Yearly Rate

The annual rate is 5%. Therefore, the half-yearly rate will be calculated as follows:

Half-Yearly Rate = (1 + Annual Rate)^(1/2) - 1

Half-Yearly Rate = (1 + 0.05)^(1/2) - 1

Half-Yearly Rate = 0.02475 or 2.475%

Step 2: Calculate the Number of Half-Yearly Periods

The time period is 2 years or 4 half-yearly periods.

Number of Half-Yearly Periods = Time Period x Frequency

Number of Half-Yearly Periods = 2 x 2

Number of Half-Yearly Periods = 4

Step 3: Calculate the Future Value

Using the compound interest formula, we can calculate the future value of ₹10000 due in 2 years at 5%pa compound interest paid half-yearly.

Future Value = Present Value x (1 + Half-Yearly Rate)^Number of Half-Yearly Periods

Future Value = ₹10000 x (1 + 0.02475)^4

Future Value = ₹10000 x 1.10416

Future Value = ₹11041.60

Step 4: Calculate the Present Value

Using the present value formula, we can calculate the present value of ₹11041.60 due in 2 years at 5%pa compound interest paid half-yearly.

Present Value = Future Value / (1 + Half-Yearly Rate)^Number of Half-Yearly Periods

Present Value = ₹11041.60 / (1 + 0.02475)^4

Present Value = ₹9249.87

Therefore, the present value of ₹10000 due in 2 years at 5%pa compound interest paid half-yearly is ₹9249.87.