The family bank stops being a spreadsheet idea the first time a kid needs $4,000 for a car and you're the one holding the money.
Write it down. Amount, rate, payment, and due date, on one page, signed by both of you. Not because you'll ever take them to court, but because the paper is what turns a handout into a loan in a nineteen-year-old's head. A verbal arrangement with your parents is a gift with a guilt tax attached.
Charge interest. Something modest, well under what a dealer would quote them, and enough that they feel it. They learn what borrowing costs, and the money comes back with a return instead of coming back flat. If your bank is a policy, that interest goes to the carrier as loan interest rather than into your pocket, so the honest version is that the family bank isn't a profit center. It's the cheapest credit your kid will ever get.
Set the payment against real income. A kid working twenty hours a week can handle $150 a month and can't handle $400. Sizing it too aggressively means you're the one who ends up renegotiating, and renegotiating with your own kid teaches the opposite lesson.
Decide in advance what happens if they stop paying. Does the car come back? Does the balance become a subtraction from what they'd inherit? Do you eat it? Any of those answers can work. Having no answer is what turns a $4,000 loan into a decade of tension at Thanksgiving.
Start smaller than a car if you can. A $600 laptop paid back over six months teaches the same lesson at a tenth of the stakes, and it tells you whether the next loan should happen at all.