Final answer:
The duration of a bond is a measure of its sensitivity to changes in interest rates, representing the weighted average time it takes to receive the bond's cash flows. Using the given information, we calculate the present value of the bond's cash flows and then use the formula for duration to find its value. In this case, the duration of the bond is approximately 2.78 years.
Step-by-step explanation:
The duration of a bond is a measure of its sensitivity to changes in interest rates. It represents the weighted average time it takes to receive the bond's cash flows, including both coupon payments and the final principal payment. The formula for calculating the duration of a bond is:
Duration = (1 * Cash Flow 1 + 2 * Cash Flow 2 + ... + n * Cash Flow n) / Present Value of Bond
In this case, the bond has a par value of $1000, a time to maturity of 3 years, and an annual coupon rate of 8%. The current yield to maturity is 10%. To calculate the duration, we need to determine the present value of the bond's cash flows. We can then use the formula to calculate the duration.
First, calculate the present value of the bond using the yield to maturity. The present value of a bond is the sum of the present values of its cash flows. The present value of a cash flow can be calculated using the formula:
Present Value = Cash Flow / (1 + Yield to Maturity)^n
For each year, we have a $80 coupon payment (8% of $1000) and the final principal payment of $1000. Using the formula above, we can calculate the present value of each cash flow and then sum them to get the present value of the bond.
Next, we use the formula for duration to calculate the weighted average time it takes to receive the bond's cash flows. The weight for each cash flow is the percentage of the bond's present value that the cash flow represents. We multiply the time to receive each cash flow by its weight, and then sum the results to get the duration of the bond.
In this case, the duration of the bond is approximately 2.78 years. Therefore, the correct answer is option b) 2.78.