Revision as of 01:05, 18 November 2023 by Admin (Created page with "Deposits of 100 are made to an account today and one year from today. The annual force of interest at time t in years for this account is: <math display = "block"> \delta_t = 0.03 + 0.005t, \, 0 \leq t \leq 3 </math> Calculate the account balance two years from today. <ul class="mw-excansopts"><li>211.07</li><li>211.87</li><li>216.05</li><li>216.79</li><li>220.24</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
Deposits of 100 are made to an account today and one year from today. The annual force of interest at time t in years for this account is:
[[math]]
\delta_t = 0.03 + 0.005t, \, 0 \leq t \leq 3
[[/math]]
Calculate the account balance two years from today.
- 211.07
- 211.87
- 216.05
- 216.79
- 220.24
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: A
The accumulated value is [math]\quad a(t)=\exp \left[\int_0^t 0.03+0.005 r d r\right]=\exp \left[0.03 t+0.0025 t^2\right][/math], The account balance is
[[math]]100 a(2)+100 \frac{a(2)}{a(1)}=100(1.0725)+100 \frac{1.0725}{1.0330}=211.07.[[/math]]
.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.