Revision as of 00:58, 18 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>12.8%</li><li>13.0%</li><li>13.2%</li><li>13.4%</li><li>13.6%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
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.
ABy Admin
Nov 18'23
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.