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.

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.