You are given the following information about a 20-year bond with face amount 7500:

• The bond has an annual coupon rate of 7.4% paid semiannually.
• The purchase price results in an annual nominal yield rate to the investor of 5.3% convertible semiannually.
• The amount for amortization of premium in the fourth coupon payment is 28.31.

Calculate the redemption value of the bond.

• 7660
• 7733
• 7795
• 7879
• 7953

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

Solution: A

The book value after the third coupon is

[[math]] 7500(0.037)a_{\overline{{{37}}}|0.0265}+C(1.0265)^{-37}=6493.05+0.379943C [[/math]]

and after the fourth coupon it is

[[math]] 7500(0.037)a_{\overline{300}|0.0265}+C(1.0265)^{-36}=6387.61+0.390012C. [[/math]]

Then

[[math]] \begin{array}{l}\\ {{6493.05+0.379943C-(6387.61+0.390012C)=28.31}}\\ {{105.44-0.01069C=28.31}}\\ {{C = 7660.15.}} \end{array} [[/math]]

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