A three-year bond with face amount X and a coupon of 4 paid at the end of every six months is priced at 90.17. A three-year bond with face value of 1.6X and a coupon of 4 paid at the end of every six months is priced at 132.47. Both have the same yield rate.

Calculate the annual nominal yield rate, convertible semiannually.

• 6%
• 8%
• 9%
• 11%
• 12%

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

Solution: E

[[math]] \begin{aligned} & 90.17=4 a_{6 j}+X v^6 \\ & 132.47=4 a_{6 j}+1.6 X v^6 \end{aligned} [[/math]]

Multiply the first equation by 1.6 :

[[math]] 144.272=6.4 a_{6 j j}+1.6 X v^6 [[/math]]

Subtract the second equation:

[[math]] 11.802=2.4 a_{6 / j} [[/math]]

Use annuity calculation on BA II Plus

[[math]] j=6 \%=\frac{i^{(2)}}{2}, i^{(2)}=12 \% [[/math]]

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