Final answer:
To find the price of a 4-year bond with a face amount of 100 and annual coupons at a rate of 5%, you need to calculate the present value of all future cash flows using the term structure of effective annual yield rates for zero coupon bonds.
Step-by-step explanation:
To find the price of a 4-year bond with a face amount of 100 and annual coupons at a rate of 5%, we need to calculate the present value of all future cash flows. First, we determine the coupon payment using the annual coupon rate and the face amount: 100 * 5% = 5. The first coupon will be paid in one year, and the remaining coupons will be paid annually for the next three years.
Using the given term structure of effective annual yield rates for zero coupon bonds, we can discount the future cash flows. The discount rate for the 4th year is 12%. We can use the formula to calculate the present value:
PV = Coupon Payment / (1 + Yield Rate)^n + Face Amount / (1 + Yield Rate)^n
Substituting the values, we have:
PV = 5 / (1 + 0.12)^1 + 100 / (1 + 0.12)^4
Simplifying the equation, we find that the price of the 4-year bond is approximately $92.47.