Earnest T needs $$900$ for his next trip to Raleigh. He has $$500$ in cash. How long in years will it take the $$500$ cash to grow to $$900$ if Earnest T earns $9\mathrm{.}3\%$ per annum on his cash, compounded quarterly? $($Enter your answers in years to $2$ decimal places, e$.$g$.,12\mathrm{.}34)$