Final answer:
The duration of the bond with an 8.4% yield to maturity and three years until maturity is 8.712 years. If the yield to maturity is 11%, the duration is 8.727 years.
Step-by-step explanation:
The duration of a bond is a measure of its price sensitivity to changes in interest rates. To calculate the duration of a bond, you can use the following formula:
Duration = (Present Value of Future Cash Flows * Time) / Bond Price
For the first part of the question, the bond has a yield to maturity of 8.4% and three years until maturity. The annual coupon payment can be calculated as 8.4% of the face value, which is $1000 * 8.4% = $84.
Using the formula, the duration of the bond is:
Duration = (($84 * 1) + ($84 * 2) + ($84 * 3) + ($1000 * 3)) / $1000 = 8.712 years.
For the second part of the question, if the yield to maturity is 11%, you can repeat the calculation using the new coupon payment amount of 11% of the face value, which is $1000 * 11% = $110. The duration of the bond in this case is:
Duration = (($110 * 1) + ($110 * 2) + ($110 * 3) + ($1000 * 3)) / $1000 = 8.727 years.