We don't have enough information to give you a good answer. To get you an accurate answer we need to know where it is.
A full housing payment generally consists of 4 or 5 parts and is referred to as PITI. This stands for principal, interest, taxes and insurance. Principal and interest payments are generally what are quoted from banks or calculators. In this case, after the $50,000 down payment the loan amount would be $450,000 and at today's low interest rates, the principal and interest payment (PI of PITI) would be about $2020.70 a month over 30 years.
The T (of PITI) is property taxes that (nationwide) average 1.5% of value per year (BE CAREFUL HERE! I have personally seen anywhere from 0.5% per year to 4% per year). So assuming your house is valued at $500,000 you'll pay about $7500 per year in property taxes which is another $625 a month (this is why the question of where is so important - taxes could run you $20,000 a year in some locations).
The final part of PITI is insurance. With less than 20% down, you'll have 2 kinds to pay. Homeowner's insurance and Private Mortgage Insurance (PMI). Homeowner's insurance should be ~$750 per year (unless in hurricane country and then multiply by 5). That's another $62.50 a month. Private mortgage insurance could easily add another $150 a month to your payment.
So the total payment with a 20% downpayment is PITI - $2020.70 + $625 + $62.50 + $150 = ~$2858.20 a month with 10% down and living in an area that does not have high homeowner's insurance or taxes (think midwest).
So, the answer to the location question is important!!