Your down payment can affect your mortgage payment in several ways. In general the more cash you put down, the smaller your monthly mortgage payment will be. Lets use a $200,000 home as an example. If you put down $40,000 (20%) for a 30-year, 4% mortgage, your monthly payment would be $764.
But, if you put down $60,000 (30%) on the same mortgage, then your monthly payment would be only be $668. This is because when you put down a larger sum, you are borrowing less, thus you need to pay back less.
In the 20% down scenario you are borrowing $160,000 and in the 30% down scenario you are only borrowing $140,000.
Your down payment can also affect your mortgage payment if you put down less than 20%. In these cases most banks require you to pay Private Mortgage Insurance (PMI). PMI helps to protect the bank if the homeowner defaults on the loan. The additional PMI payment will increase the monthly mortgage payment.
Using our $200,000 home above as an example, if you put 10% down, your monthly payment would be $859 and your PMI would be about $81 for a total monthly payment of $940.
On the plus side, PMI allows the potential homeowner to purchase the home with less money down.
Keep in mind that these calculations do not include property taxes or homeowners insurance, which would also increase your monthly payment.