An n-year bond with an annual coupon rate of r % has the following characteristics:

1. The face amount is 980.
2. Coupons of 49 are paid semiannually.
3. The annual nominal yield rate convertible semiannually is (r + 1.8)%.
4. The purchase price is 915.70.
5. The redemption value is 1000.

Calculate n.

• 2
• 3
• 4
• 5
• 6

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

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.