How Do I Calculate Mortgage Payments When Buying A Home From A Family Member?

We are thinking of purchasing a house from my father. Instead of using a mortgage broker or bank, he suggested using a lawyer to set up monthly mortgage payments directly to him. We would still buy the house, and it would be in our names, not renting. How are payments like this calculated? Also, it seems this gives us flexibility and saves us money, but isn’t as secure. What are the specific down-sides to this?