Earnest T needs $$870$ for his next trip to Raleigh. He has $$520$ in cash. How long in years will it take the $$520$ cash to grow to $$870$ if Earnest T earns $7\mathrm{.}0\%$ per annum on his cash, compounded quarterly? $($Enter your answers in years to $2$ decimal places, e$.$g$.,12\mathrm{.}34)$