Purchase Price of a ₹1000 Bond

To find the purchase price of a ₹1000 bond redeemable at a 4% annual dividend rate with a yield rate of 5%, we need to calculate the present value of the bond's future cash flows.

Understanding the Terms:
- Face Value of the Bond (FV): ₹1000
- Dividend Rate (DR): 4% per annum
- Yield Rate (YR): 5% per annum

Calculating the Present Value of the Dividends:
The dividend payments are made annually, so we can calculate the present value of each dividend payment using the formula:
Present Value (PV) = Dividend Payment / (1 + Yield Rate)^n

Where:
- Dividend Payment: ₹1000 * Dividend Rate = ₹40
- Yield Rate: 5% = 0.05
- n: the number of years until the bond matures

Calculating the Present Value of the Redemption Amount:
The redemption amount is the face value of the bond, which is ₹1000. We can calculate its present value using the formula:
Present Value (PV) = Redemption Amount / (1 + Yield Rate)^n

Calculating the Total Present Value:
To find the purchase price of the bond, we sum up the present values of the dividends and the redemption amount:
Total Present Value = Sum of Present Values of Dividends + Present Value of Redemption Amount

Example Calculation:
Let's assume the bond matures in 5 years (n = 5).

Step 1: Calculating the Present Value of the Dividends:
PV of Dividends = ₹40 / (1 + 0.05)^1 + ₹40 / (1 + 0.05)^2 + ₹40 / (1 + 0.05)^3 + ₹40 / (1 + 0.05)^4 + ₹40 / (1 + 0.05)^5

Step 2: Calculating the Present Value of the Redemption Amount:
PV of Redemption Amount = ₹1000 / (1 + 0.05)^5

Step 3: Calculating the Total Present Value:
Total Present Value = PV of Dividends + PV of Redemption Amount

Step 4: Determining the Purchase Price:
The purchase price of the bond is equal to the Total Present Value.

Conclusion:
By calculating the present value of the dividends and the redemption amount and summing them up, we can find the purchase price of the ₹1000 bond redeemable at a 4% annual dividend rate with a yield rate of 5%.