A four-year 1000 face amount bond, with an annual coupon rate of 5% paid semiannually, has redemption value of C. It is bought at a price to yield an annual nominal rate of 6% convertible semiannually. If the term of the bond had been two years, the purchase price would have been 7% less.

Calculate C.

• 455
• 469
• 541
• 611
• 626

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

Solution: A

From the first bond: [math]P=25 a_{\overline{8} 0.03}+C v^8[/math] From the second bond: [math]0.93 P=25 a_{\overline{4} \mid 0.03}+C v^4[/math] Multiply the first equation by 0.93 and plug into the second equation:

[[math]] \begin{aligned} & 0.93(25) a_{\overline{8}|0.03}+0.93 C=25 a_{\overline{4}|0.03}+C v^4 \\ & 163.2078+0.73415 C=92.9275+0.88849 C \\ & 70.2804=0.15434 C \\ & C=455.37 \end{aligned} [[/math]]

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