Bond X is a 20-year bond with annual coupons and the following characteristics:

Calculate the maximum purchase price for Bond X that will guarantee an annual effective yield rate of at least 5%.

• 1519
• 1542
• 1570
• 1596
• 1623

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

Solution: B

Because the yield is less than the coupon rate, the bond sells at a premium and the worst case for the buyer is an early call. Hence the price should be calculated based on the bond being called at time 16. The price is

[[math]] 100a_{\overline{{{16}}}|0.05}+1000(1.05)^{-16}=100(10.0378)+458.11=1542\,. [[/math]]

(When working with callable bonds, the maximum a buyer will pay is the smallest price over the various call dates. Paying more may not earn the desired yield.)

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