You have decided to invest in a newly issued 20-year bond with annual coupons and the following characteristics:

1. The price at issue is 1321.
2. The face amount is 1111.
3. The annual coupon rate is 10%.
4. The bond is callable for 1111 immediately after the payment of either the 18 th or 19th coupon.

Calculate the minimum possible annual effective yield rate that you can earn.

• 7.881%
• 7.937%
• 7.985%
• 8.028%
• 8.065%

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

Solution: C

The minimum yield will occur at the earliest redemption date since the bond is brought at a premium. Therefore [math]\mathrm{n}=18[/math].

[[math]] \begin{aligned} & 1321=111.10 a_{\overline{18} \mid i}+1111 v^{18} \\ & i=0.07985 \end{aligned} [[/math]]

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