Matthew deposits $100$ into Fund X$,$ which earns a nominal annual rate of discount of $12\%$ convertible quarterly. At the same time, Sarah deposits $200$ into Fund Y$,$ which earns a constant annual force of interest of $0\mathrm{.}08.$ After n years, the balance of Fund X equals the balance of Fund Y$.$ Calculate n$.$Matthew deposits $100$ into Fund X$,$ which earns a nominal annual rate of discount of $12\%$ convertible quarterly.

At the same time, Sarah deposits $200$ into Fund Y$,$ which earns a constant annual force of interest of $0\mathrm{.}08.$

After $n$ years, the balance of Fund $x$ equals the balance of Fund $Y.$

Calculate $n.$

$14\mathrm{.}5$

$16\mathrm{.}6$

$17\mathrm{.}6$

$18\mathrm{.}1$

$18\mathrm{.}6$