A blue boat costs $$20,000\mathrm{.}20$ and you agree to pay it off with $36$ level payments of Q at the end of each month. The sales person then offers you a gold boat for $$22,376\mathrm{.}42.$ How long would it take you to pay off the gold boat with level end of month payments of Q$?$ The nominal interest rate for both transactions is i $=9\%$ convertible monthly.