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.

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.