Your coin collection contains $531942$ silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in $2045,$ assuming they appreciate at an annual rate of $8$ percent?

Multiple Choice

$$139,523\mathrm{.}16$

$$149,803\mathrm{.}81$

$$146,866\mathrm{.}48$

$$15,284\mathrm{.}25$

$$142,460\mathrm{.}49$