How much would $$20,000$ due in $50$ years be worth today if the discount rate were $7\mathrm{.}5\%?$

a$.$ $$661\mathrm{.}47$

b$.$ $$618\mathrm{.}45$

c$.$ $$451\mathrm{.}74$

d$.$ $$656\mathrm{.}09$

e$.$ $$537\mathrm{.}78$