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Jane Smith has $$20,000$ in a brokerage account, and she plans to contribute an additional $$7,500$ to the account at the end of every year. The brokerage account has an expected annual return of $8\%.$ If Jane$$s goal is to accumulate $$375,000$ in the account, how many years will it take for Jane to reach her goal?

$5\mathrm{.}20$

$18\mathrm{.}40$

$16\mathrm{.}33$

$12\mathrm{.}50$

$10\mathrm{.}00$