A "Name That Tune" contest has a grand prize of $$500,000.$ However, the contest stipulates that the winner will receive just $$200,000$ immediately, and $$30,000$ at the end of each of the next $10$ years. Assuming that one can earn $8\%$ on their money, how much has the contest winner actually won?

a$.$ $$250,000\mathrm{.}00$

b$.$ $$309,225\mathrm{.}11$

c$.$ $$365,826\mathrm{.}02$

d$.$ $$401,302\mathrm{.}44$

e$.$ $$500,000\mathrm{.}00$