Toby purchased a 20-year par value bond with semiannual coupons of 40 and a redemption value of 1100. The bond can be called at 1200 on any coupon date prior to maturity, starting at the end of year 15.

Calculate the maximum price of the bond to guarantee that Toby will earn an annual nominal interest rate of at least 6% convertible semiannually.

• 1251
• 1262
• 1278
• 1286
• 1295

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

Solution: B

Because 40/1200 is greater than 0.03, for early redemption the earliest redemption should be evaluated. If redeemed after 15 years, the price is

[[math]]40a_{\overline{40}|0.03} + 1200/1.03^{30} = 1278.40[[/math]]

. If the bond is redeemed at maturity, the price is

[[math]]40a_{\overline{40}|0.03} + 1100/1.03^{40} = 1261.80[[/math]]

. The smallest value should be selected, which is 1261.80. (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.