An investor purchases a 30-year bond with a face amount of 1000 and annual coupon rate of 8% paid semi-annually. The bond is callable at its face value any time following the coupon payment occurring at the end of the 15th year. The bond is bought at a premium based on an annual effective yield rate of 7%.

Calculate the purchase price of the bond.

• 1067
• 1104
• 1132
• 1141
• 1154

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

Solution: B

Since the bond is bought at a premium and redemption will occur to the investor’s greatest disadvantage, assume the bond is called at the earliest possible redemption date, or simultaneous with the coupon payment occurring at the end of the 15th year. The cash flows then become a bond paying semiannual coupons of 40 for 15 years and returning 1000 at the end of the 15 th year. At a yield of 7% effective annually:

[[math]] \begin{aligned} & 1.07=\left[1+\frac{i^{(2)}}{2}\right]^2 \\ & \frac{i^{(2)}}{2}=0.034408 \\ & P=40 a_{\overline{30}|}+1000 v^{30} \\ & P=1103.61 \end{aligned} [[/math]]

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