An investor purchased a 25-year bond with semiannual coupons, redeemable at par, for a price of 10,000. The annual effective yield rate is 7.05%, and the annual coupon rate is 7%.

Calculate the redemption value of the bond.

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

• 9,918
• 9,942
• 9,981
• 10,059
• 10,083

Solution: A

Let j = periodic yield rate, r = periodic coupon rate, F = redemption (face) value, P = price, n = number of time periods, and v_j = 1/(1+j). In this problem, j = (1.0705)^1/2-1 = 0.03465, r = 0.035, P=10,000, and n = 50.

The present value equation for a bond is yields

[[math]]P = Fv^n + Fr a_{\overline{n}|j} [[/math]]

; solving for the redemption value F yields

[[math]] F={\frac{P}{v_{j}^{n}+r a_{{\overline{{{n}}}}|i}}}={\frac{10,000.}{\left(1.03465\right)^{30}+0.035a_{\overline{50}|0.03465}}}={\frac{10,000}{0.18211+0.035(23.6044)}}=9,918. [[/math]]

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