Revision as of 18:43, 19 November 2023 by Admin (Created page with "An n-year bond with annual coupons has the following characteristics: *The redemption value at maturity is 1890; *The annual effective yield rate is 6%; *The book value immediately after the third coupon is 1254.87; and *The book value immediately after the fourth coupon is 1277.38. Calculate n. <ul class="mw-excansopts"><li>16</li><li>17</li><li>18</li><li>19</li><li>20</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
An n-year bond with annual coupons has the following characteristics:
- The redemption value at maturity is 1890;
- The annual effective yield rate is 6%;
- The book value immediately after the third coupon is 1254.87; and
- The book value immediately after the fourth coupon is 1277.38.
Calculate n.
- 16
- 17
- 18
- 19
- 20
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: E
Book values are linked by BV3(1 + i) – Fr = BV4. Thus 1254.87(1.06) – Fr = 1277.38. Therefore, the coupon is Fr = 52.7822. The prospective formula for the book value at time 3 is
[[math]]
\begin{array}{l}{{1254.87=52.7822{\frac{1-1.06^{-(n-3)}}{0.06}}+1890(1.06)^{-(n-3)}}}\\ {{375.1667=1010.297(1.06)^{-(n-3)}}}\\ {{n-3={\frac{1}{-1}}{\frac{1}{75.1667/1010.297)}}=17.}}\end{array}
[[/math]]
Thus, n = 20. Note that the financial calculator can be used to solve for n – 3.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.