Revision as of 21:14, 19 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>110</li><li>114</li><li>122</li><li>128</li><li>132</li></ul> {{soacopyright | 2023 }} {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
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.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
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.