How many years would it take to save $$1,000,000$ if you deposit $$2,000$ at the end of each month that pays $12$ percent per year? $($hint: compute the monthly rate using simple average; monthly deposit and final balance have different signs, deposit is kind of "cash outflow from your pocket to your bank account". $)$

$16$ years

$12$ years

$15$ years

$13$ years