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.

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.