$2.$ Your grandmother invested a lump sum $20$ years ago at $4\mathrm{.}25\%$ interest. Today, she gave you the proceeds of that investment which totaled $$51,480\mathrm{.}79.$ How much did she originally invest?

a$.$ $$18,500\mathrm{.}00$

b$.$ $$17,444\mathrm{.}86$

c$.$ $$19,939\mathrm{.}45$

d$.$ $$22,393\mathrm{.}61$

e$.$ $$17,500\mathrm{.}00$