A 20-year non-callable bond that pays coupons annually has a face amount of 2000. The bond was bought at a price of 2300 and has an annual effective yield rate of 7%. A 20-year callable bond with the same annual coupon rate and face amount is callable for 2000 at the end of the 18th or 19th year.

Calculate the maximum price of the callable bond that guarantees an annual effective yield of at least 7%.

• 2268
• 2276
• 2285
• 2293
• 2300

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

Solution: C

Let [math]r[/math] be the coupon rate.

[[math]] \begin{aligned} & 2300=2000 r a_{\overline{20}|0.07}+2000 v^{20} \\ & 2000 r=168.32 \end{aligned} [[/math]]

Bond is bought at a premium, so assume called as early as possible at year 18 .

[[math]] \begin{aligned} & P=168.32 a_{\overline{18}|0.07}+2000 v^{18} \\ & P=2284.85 \end{aligned} [[/math]]

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