On July 1, 2004, a person invested $1,000 in a fund for which the force of interest at time $t$ is given by $\delta_t = \frac{2 + 4 t}{50}$, where $t$ is the number of years since January 1, 2004. Determine the accumulated value of the investment on January 1, 2005.
Accumulated value of the investment = $