How do you get 200 years? Money in the stock market makes returns.
Use this calculator
Put in $5,000 payment
Nothing at start.
43 years (65 - 22), 6.3%
Do this in an IRA so there are no taxes involved.
You will have $1,018,527 at the end.
6.3% is reasonable. I have been averaging over 8% for last 20 years including the big meltdowns.