Revision as of 18:44, 19 November 2023 by Admin (Created page with "An n-year bond with semiannual coupons has the following characteristics: *The par value and redemption value are 2500; *The annual coupon rate is 7% payable semi-annually; *The annual nominal yield to maturity is 8% convertible semiannually; and *The book value immediately after the fourth coupon is 8.44 greater than the book value immediately after the third coupon. Calculate n. <ul class="mw-excansopts"><li>6.5</li><li>7.0</li><li>9.5</li><li>12.0</li><li>14.0</li>...")
ABy Admin
Nov 19'23
Exercise
An n-year bond with semiannual coupons has the following characteristics:
- The par value and redemption value are 2500;
- The annual coupon rate is 7% payable semi-annually;
- The annual nominal yield to maturity is 8% convertible semiannually; and
- The book value immediately after the fourth coupon is 8.44 greater than the book value immediately after the third coupon.
Calculate n.
- 6.5
- 7.0
- 9.5
- 12.0
- 14.0
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: A
Book values are linked by BV3(1 + i) – Fr = BV4. Thus BV3(1.04) – 2500(0.035) = BV3 + 8.44. Therefore, BV3 = [2500(0.035) + 8.44]/0.04 = 2398.5. The prospective formula for the book value at time 3 is, where m is the number of six-month periods.
[[math]]
\begin{array}{l}{{2398.5=2500(0.035){\frac{1-1.04^{-(m-3)}}{0.04}}+2500(1.04)^{-(m-3)}}}\\ {{\mathrm{211=312.5(1.04)^{-(m-3)}}+2500(1.04)^{-(m-3)}}}\\ {{m-3={\frac{\ln(211/312.5)}{-\ln(1.04)}}=10.}}\end{array}
[[/math]]
Thus, m = 13 and n = m/2 = 6.5. Note that the financial calculator can be used to solve for m – 3.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.