Revision as of 18:29, 19 November 2023 by Admin (Created page with "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. {{soacopyright | 2023 }} <ul class="mw-excansopts"><li>9,918</li><li>9,942</li><li>9,981</li><li>10,059</li><li>10,083</li></ul>")
ABy Admin
Nov 19'23
Exercise
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
ABy Admin
Nov 19'23
Solution: A
Let j = periodic yield rate, r = periodic coupon rate, F = redemption (face) value, P = price, n = number of time periods, and vj = 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.