A ten-year bond with a face amount of 1000, a redemption value of C, and an annual coupon rate of 7% paid semiannually is purchased at a discount to yield an annual nominal rate of 7.5%, convertible semiannually. The accumulation of discount in the 12th coupon is 7.

Calculate C.

• 673
• 799
• 1193
• 1344
• 1540

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

Solution: C

[[math]]\begin{aligned} & 7=P_{12}=C(i-g) v^{20-12+1} \\ & 7=[C i-C g]\left(\frac{1}{0.0375}\right)^9 \\ & 9.7497=C i-F r \\ & 9.7497=C(0.0375)-35 \\ & C=1193.33\end{aligned}[[/math]]

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