A 20-year bond with 8% annual coupons is purchased at a price of P. The face amount of the bond is F. The price assumes an annual effective yield rate of 4%. The change in book value of the bond during the 8th year is equal to 43.24.

Calculate P.

• 2315
• 2470
• 2625
• 2780
• 3085

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: D

[[math]]\begin{gathered}\text { Adjustment in book value }=(g-i) v_i^{n-t+1} F \\ =(0.08-0.04) v_{0.04}^{13} F=43.24 \\ F=1800 \\ P=1800(0.08) a_{\overline{20} \mid 0.04}+1800 v_4^{20} \\ =144 a_{\overline{20}|0.04}+1800 v_4^{20}=2778.50\end{gathered}[[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.