A zero-coupon bond with a face value of 1000 sells for a price of 600 and matures in n years, where n is a whole number. A second bond has the same price, same time until maturity, and same annual effective yield. It pays annual coupons at an annual rate equal to 50% of the annual effective yield rate.

Calculate the face value of the second bond.

• 666.67
• 750.00
• 774.60
• 800.00
• 826.40

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

Solution: B

[[math]]\begin{aligned} & 600(1+i)^n=1000 \\ & (1+i)^n=\frac{10}{6} \\ & v^n=0.6 \\ & 600=F \frac{i}{2} a_{\overline{n}|i}+F v^n \\ & 600=F\left[\frac{i}{2} \frac{1-v^n}{i}+v^n\right] \\ & 600=F\left[\frac{1}{2}(1-0.6)+0.6\right] \\ & F=750\end{aligned}[[/math]]

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