A 15-year bond with semiannual coupons is purchased for 2895.28. The bond is redeemable for 1000. The first coupon payment is equal to R and each subsequent coupon is 1% larger than the previous coupon payment. The annual nominal yield rate on this bond is 6.2% convertible semiannually.

Calculate R.

• 110
• 114
• 122
• 128
• 132

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

Solution: B

[[math]] \begin{aligned} & 2895.28=R v+R(1.01) v^2+R(1.01)^2 v^3+\ldots+R(1.01)^{29} v^{30}+1000 v^{30} \\ & \implies R\left[\frac{1-\left(\frac{1.01}{1.031}\right)^{30}}{0.031-0.01}\right]+1000 v^{30}=2895.28 \\ & \implies R=113.75\end{aligned} [[/math]]

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