Arianne estimates that her investment strategy will pay her $14\mathrm{.}00\%,$ compounded quarterly. If she is investing $$10,500$ today, in how many years will she reach her goal of $$22,000?$

$5\mathrm{.}4$ years

$7\mathrm{.}2$ years

$5\mathrm{.}2$ years

$5\mathrm{.}0$ years

$5\mathrm{.}3$ years