Revision as of 01:12, 18 November 2023 by Admin (Created page with "The annual force of interest is <math>\delta_t=\frac{2}{10-t}</math>, for <math>0 \leq t<10</math>, in which <math>t</math> is measured in years. Calculate the equivalent annual nominal discount rate compounded every two years for the period <math>2.0 \leq t \leq 2.4</math>. <ul class="mw-excansopts"><li>1,758</li><li>1,828</li><li>1,901</li><li>2,078</li><li>2,262</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
The annual force of interest is [math]\delta_t=\frac{2}{10-t}[/math], for [math]0 \leq t\lt10[/math], in which [math]t[/math] is measured in years.
Calculate the equivalent annual nominal discount rate compounded every two years for the period [math]2.0 \leq t \leq 2.4[/math].
- 1,758
- 1,828
- 1,901
- 2,078
- 2,262
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: A
[[math]]\left(1-\frac{d^{(1 / 2)}}{0.5}\right)^{-0.5(0.4)}=\exp \left(\int_{2.0}^{2.4} \frac{2}{10-t} d t\right)[[/math]]
[[math]]
\begin{aligned}
& \left(1-2 d^{(1 / 2)}\right)^{-0.2}=\exp \left[-\left.2 \ln (10-t)\right|_{2.0} ^{2.4}\right] \\
& \left(1-2 d^{(1 / 2)}\right)^{-0.2}=\left(\frac{8}{7.6}\right)^2 \\
& d^{(1 / 2)}=0.20063
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.