Revision as of 01:17, 18 November 2023 by Admin (Created page with "You are given that the force of interest at time t (in years) is <math>\frac{1}{t+8}</math> Calculate the annual effective rate of interest in year 5. <ul class="mw-excansopts"><li>6.2%</li><li>6.6%</li><li>7.4%</li><li>8.3%</li><li>9.5%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
You are given that the force of interest at time t (in years) is [math]\frac{1}{t+8}[/math]
Calculate the annual effective rate of interest in year 5.
- 6.2%
- 6.6%
- 7.4%
- 8.3%
- 9.5%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: D
[[math]]
\begin{aligned} & a(t)=\exp \left(\int_0^t \frac{1}{r+8} d r\right) \\ & =\exp \left[\left.\ln (t+8)\right|_0 ^t\right] \\ & =\exp [\ln (t+8)-\ln (8)] \\ & =\exp \left(\ln \frac{t+8}{8}\right)=\frac{t+8}{8} \\ & \frac{a(5)}{a(4)}=\frac{13 / 8}{12 / 8}=1.08333 \\ & i_5=0.08333\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.