A vehicle payment plan agreement is a contract between a buyer and seller of a vehicle that agrees to installment payments. If so, Georgia law requires that the finance agreement be in writing in a retail installment contract.A car sale payment agreement is used when the purchase price of the car is paid in instalments. What should you put in my car sale contract with payments? Though not recommended, you can also stipulate an agreed to payment plan. An appropriate Car Payment Agreement Letter can be quite simple to understand; however, there are certain factors that are to be kept in mind over its purchase.