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.

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.