Revision as of 23:01, 17 November 2023 by Admin (Created page with "Payments are made to an account at a continuous rate of <math>100e^{0.5t}</math> from time t = 1 to time t = 3. The force of interest for this account is <math>\delta = 8\%</math>. Calculate the value of the account at time t = 4. <ul class="mw-excansopts"><li>313</li><li>432</li><li>477</li><li>606</li><li>657</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 17'23
Exercise
Payments are made to an account at a continuous rate of [math]100e^{0.5t}[/math] from time t = 1 to time t = 3. The force of interest for this account is [math]\delta = 8\%[/math].
Calculate the value of the account at time t = 4.
- 313
- 432
- 477
- 606
- 657
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 17'23
Solution: E
The accumulated value to time 4 is
[[math]]
\int_{1}^{3}100e^{0.5t}e^{0.88(4-t)}d t=100e^{0.32}\int_{1}^{3}e^{0.42t}d t=100e^{0.32}\frac{e^{0.42t}}{0.42}\biggl|_{1}^{3}=\frac{100e^{0.32}(e^{1.26}-e^{0.42})}{0.42}=657.
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.