Final answer:
The bond's price is $1124.84. The bond's duration is 4.46 years. The effect on the bond is -12.55.
Step-by-step explanation:
a) To calculate the bond's price, we need to find the present value of its future cash flows. The bond pays an 8% coupon at the end of each year for five years, and has a yield of 11%. Using the formula for the present value of an annuity, the bond's price can be calculated as follows:
Price = (Coupon Payment / Yield) * (1 - 1 / (1 + Yield)^n) + Face Value / (1 + Yield)^n
Substituting the given values into the formula, we get:
Price = (0.08 * 5000 / 0.11) * (1 - 1 / (1 + 0.11)^5) + 5000 / (1 + 0.11)^5 = $1124.84
Therefore, the bond's price is $1124.84.
b) The bond's duration measures its sensitivity to changes in interest rates. It can be calculated using the formula:
Duration = [(1 * Coupon Payment) / Price] + [(2 * Coupon Payment) / Price] + ... + [(n * Coupon Payment + Face Value) / Price]
Substituting the given values into the formula, we get:
Duration = [(1 * 0.08 * 5000) / 1124.84] + [(2 * 0.08 * 5000) / 1124.84] + [(3 * 0.08 * 5000) / 1124.84] + [(4 * 0.08 * 5000) / 1124.84] + [(5 * (0.08 * 5000 + 5000)) / 1124.84] = 4.46
Therefore, the bond's duration is 4.46 years.
c) To calculate the effect on the bond, we can use the following formula:
Effect = - Duration * (Change in Yield) * (Price / (1 + Yield))
Substituting the given values into the formula, we get:
Effect = - 4.46 * (0.11 - 0.08) * (1124.84 / (1 + 0.11)) = - 12.55
Therefore, the effect on the bond is -12.55.