On July 1, 1999, a person invested 1000 in a fund for which the force of interest at time [math]t[/math] is given by [math]\delta_t=\frac{3+2 t}{50}[/math], where [math]t[/math] is the number of years since January 1, 1999. Determine the accumulated value of the investment on January 1, 2000.

• 1036
• 1041
• 1045
• 1046
• 1051

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

Solution: D

[[math]] \begin{aligned} \textrm{AccAmt} & =1000 * \exp \left(\int_{.5}^1 \frac{3+2 t}{50}\right)=1000 * \exp \left(\left.\frac{3 t+t^2}{50}\right|_{.5} ^1\right) \\ & =1000 * \exp ((4-7 / 4) / 50)=1046.028 \end{aligned} [[/math]]

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.