An investor deposits 150 today and receives 100 one year from now and 80 two years from now. Calculate the annual nominal rate of interest convertible quarterly that the investor earns.

• 12.8%
• 13.0%
• 13.2%
• 13.4%
• 13.6%

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

Solution: B

[[math]] \begin{aligned} & 150=100 v+80 v^2 \\ & 80 v^2+100 v-150=0 \\ & v=\frac{-100 \pm \sqrt{100^2-4(80)(-150)}}{160} \\ & v=0.880199 \\ & i=0.136106 \\ & 1.136106=\left[1+\frac{i^{(4)}}{4}\right]^4 \\ & i^{(4)}=0.129664\end{aligned} [[/math]]

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