A ten-year 100 face amount bond has an annual coupon rate of 8% payable semiannually. The bond is callable at the end of the 5th , 7th , and 9th years at par, immediately after the coupon payment.

Calculate the maximum price of the bond that ensures an annual effective yield of at least 6%.

• 108.92
• 111.83
• 114.41
• 115.59
• 116.74

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: A

Since the coupon rate per coupon payment period 4% is greater than the effective rate of interest per coupon payment period 2.9563%, it is to the disadvantage of the bond holder to have the bond redeemed at an early date. Hence, we only need to calculate the present value of such a bond at the worst-case scenario, which is that the bond is called at the end of the 5 th year.

[[math]] \begin{aligned} & P=4 a_{100.029563}+100 v^{10} \\ & P=108.92 \end{aligned} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.