Revision as of 18:26, 19 November 2023 by Admin (Created page with "An investor owns a bond that is redeemable for 300 in seven years. The investor has just received a coupon of 22.50 and each subsequent semiannual coupon will be X more than the preceding coupon. The present value of this bond immediately after the payment of the coupon is 1050.50 assuming an annual nominal yield rate of 6% convertible semiannually. Calculate X. <ul class="mw-excansopts"><li>7.54</li><li>10.04</li><li>22.37</li><li>34.49</li><li>43.98</li></ul> {{soac...")
ABy Admin
Nov 19'23
Exercise
An investor owns a bond that is redeemable for 300 in seven years. The investor has just received a coupon of 22.50 and each subsequent semiannual coupon will be X more than the preceding coupon. The present value of this bond immediately after the payment of the coupon is 1050.50 assuming an annual nominal yield rate of 6% convertible semiannually.
Calculate X.
- 7.54
- 10.04
- 22.37
- 34.49
- 43.98
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: A
[[math]]
\begin{align*}
1050.50=(22.50+X)a_{\overline{14}|0.03}+ X\left({\frac{a_{\overline{14}|0.03}-14(1.03)^{-14}}{0.03}}\right)
+300(1.03)^{-14} \\
1050.50=(22.50+X)11.2961+X\left({\frac{11.2961-9.25565}{0.03}}\right)+198.335 \implies 79.3111X \implies 598=7.54
\end{align*}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.