Revision as of 21:15, 19 November 2023 by Admin (Created page with "An n-year bond with an annual coupon rate of r % has the following characteristics: # The face amount is 980. # Coupons of 49 are paid semiannually. # The annual nominal yield rate convertible semiannually is (r + 1.8)%. # The purchase price is 915.70. # The redemption value is 1000. Calculate n. <ul class="mw-excansopts"><li>2</li><li>3</li><li>4</li><li>5</li><li>6</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
An n-year bond with an annual coupon rate of r % has the following characteristics:
- The face amount is 980.
- Coupons of 49 are paid semiannually.
- The annual nominal yield rate convertible semiannually is (r + 1.8)%.
- The purchase price is 915.70.
- The redemption value is 1000.
Calculate n.
- 2
- 3
- 4
- 5
- 6
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: E
[[math]]
\begin{aligned} & r=\frac{49}{980}(2)=0.10 \\ & i^{(2)}=0.10+0.018=0.118 \\ & \frac{i^{(2)}}{2}=0.059 \\ & 915.70=49 a_{\overline{2n} \mid 0.059}+1000 v^{2 n} \\ & 2 n=12 \\ & n=6\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.