To calculate the realized rate of return on the bond, we need to account for both the annual interest payments (coupon payments) and the capital gain (the difference between the selling price and the purchase price). Here's the step-by-step process:

Step 1: Identify the known values.

• Purchase price of the bond: $P_0 = 909$
• Selling price of the bond: $P_T = 964$
• Annual coupon payment: $C = 65$
• Number of years held: $T = 5$

Step 2: Calculate the total dollar return.

The total return includes both the capital gain and the interest payments.

• Capital gain = Selling price − Purchase price = $964 - 909 = 55$
• Total interest received = Annual interest × Number of years = $65 \times 5 = 325$

Thus, the total dollar return is: $\text{Total Return} = \text{Capital gain} + \text{Total interest received} = 55 + 325 = 380$

Step 3: Calculate the realized rate of return.

The realized rate of return is the total return divided by the initial investment over the investment period:

$\text{Realized rate of return} = \frac{\text{Total return}}{P_0} \times 100 = \frac{380}{909} \times 100 \approx 41.82\%$

Thus, the realized rate of return over the 5 years is approximately 41.82%.

Step 4: Annualize the realized rate of return.

To find the annualized rate of return, we use the following formula: $\text{Annualized rate of return} = \left( 1 + \frac{\text{Total return}}{P_0} \right)^{\frac{1}{T}} - 1$ Substitute the values: $\text{Annualized rate of return} = \left( 1 + \frac{380}{909} \right)^{\frac{1}{5}} - 1$

Let me calculate this for you.The annualized realized rate of return on the bond is approximately 7.24%.

Would you like more details on this calculation or have any other questions?

Here are 5 related questions you might find useful:

1. How do you calculate the present value of a bond?
2. What is the difference between coupon rate and yield to maturity?
3. How do changes in interest rates affect bond prices?
4. What is the difference between nominal return and real return on bonds?
5. How do you calculate the internal rate of return (IRR) on an investment?

Tip: When evaluating bond returns, always consider both the interest payments and any capital gains or losses, as they both impact the total return.