excans:878843ad3c: Difference between revisions

Latest revision as of 18:35, 19 November 2023

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]]

@@ Line 1: / Line 1: @@
-An investor purchased a 25-year bond with semiannual coupons, redeemable at par, for a price of
+'''Solution: A'''
-,000. The annual effective yield rate is 7.05%, and the annual coupon rate is 7%.
-Calculate the redemption value of the bond.
+Let j = periodic yield rate, r = periodic coupon rate, F = redemption (face) value, P = price, n =
+number of time periods, and v<sub>j</sub> = 1/(1+j). In this problem, j = (1.0705)<sup>1/2</sup>-1 = 0.03465, r = 0.035, P=10,000, and n = 50.
+The present value equation for a bond is
+yields <math display = "block">P = Fv^n + Fr a_{\overline{n}|j}  </math>; solving for the redemption value F
+yields
+<math display = "block">
+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>
 {{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>