You expect to receive a payout from a trust fund in $4$ years. The payout will be for $$12,000.$ You plan to invest the money at an annual rate of $6\mathrm{.}2$ percent until the account is worth $$20,500.$ How many years do you have to wait from today?

$11\mathrm{.}61$ years

$8\mathrm{.}90$ years

$12\mathrm{.}90$ years

$11\mathrm{.}47$ years

$9\mathrm{.}68$ years