Most major banks will have relationship pricing incentives for customers who have depository relationships with them. Banks realize that helping a person finance a home purchase is one of life’s key moments, so they want to do everything possible to be involved.
As a result, banks will often have tiered incentive levels depending on the amount of cash the customer has deposited with the bank. For example, a major bank headquartered in NYC told us that they’ll reduce a borrower’s mortgage interest rate by 1/8% with a $50,000 deposit at close, and by 3/8% with a $200,000 deposit at close. They also mentioned that you could move the money from your checking account the day after closing without penalty!