Josie has some old artwork that she hopes to sell for $$15,600$ in the future $($FV$).$ She was just offered $$6,000$ for all of the artwork $($PV$).$ At a discount rate of $7\%$ with quarterly compounding, how many years would Josie have to wait if she wanted to sell for the $$15,600?$

Group of answer choices

$14\mathrm{.}12$ years

$56\mathrm{.}49$ years

$55\mathrm{.}08$ years

$13\mathrm{.}77$ years