Revision as of 20:59, 19 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>455</li><li>469</li><li>541</li><li>611</li><li>626</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
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.
ABy Admin
Nov 19'23
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.