Revision as of 19:16, 19 November 2023 by Admin (Created page with "Let A and B be bonds with semiannual coupons as described in the table below: {| class="table" ! Bond !! Price !! Annual coupon rate !! Par !! Years to redemption !! Annual nominal yield rate convertible semiannually |- | A || X || 8% || 1000 || 5 || 6% |- | B || X || y || 1000 || 5 || 7% |} Calculate y. <ul class="mw-excansopts"><li>8.45%</li><li>8.65%</li><li>8.85%</li><li>9.05%</li><li>9.25%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
Let A and B be bonds with semiannual coupons as described in the table below:
| Bond | Price | Annual coupon rate | Par | Years to redemption | Annual nominal yield rate convertible semiannually |
|---|---|---|---|---|---|
| A | X | 8% | 1000 | 5 | 6% |
| B | X | y | 1000 | 5 | 7% |
Calculate y.
- 8.45%
- 8.65%
- 8.85%
- 9.05%
- 9.25%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: D
Let C be the amount of the semiannual coupon for bond B.
[[math]]
\begin{array}{l}{{{ X}=40a_{\overline{100}|0.03}+1000(1.03)^{-10}=1085.30}}\\ {{{ X}=1085.30=C a_{\bar{1}00.035}+1000(1.035)^{-10}=8.3166C+708.9188}}\\ {{{ C}=(1085.30-708.9188)/8.3166=45.2566}}\\ {{{ Y}=\frac{45.25660 \times 2}{1000}=.0905=9.059 \%}}\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.