A vehicle payment plan agreement is a contract between a buyer and seller of a vehicle that agrees to installment payments. The subscription fee must provide a person exclusive use of an agreed-upon number of motor vehicles at any given time during the full term of the subscription.Watch this before you finance your next car (former dealer explains how to read a purchase contract) To draft a legal payment agreement for a vehicle sale, it's essential to include specific details and terms to protect both the buyer and the seller.