A lease payment is not a loan payment
Buying a car on finance means borrowing its whole price and repaying it. Leasing means paying for the part of the car you actually use up, plus a charge on the money the leasing company has tied up in the rest. There is no balance, nothing is being repaid, and at the end you hand the car back.
That is why the arithmetic is different and why a loan calculator gives the wrong answer for a lease. The payment is depreciation, the value lost over the term, plus a rent charge on the money involved. Those two halves move in opposite directions as the residual changes, which is the part that surprises people.
The residual decides almost everything
The residual is what the car is agreed to be worth when the lease ends. The leasing company sets it from a published guide and it is not negotiable, and it does more to the payment than any other number on the sheet.
A car that holds its value well has a high residual, loses little over the term, and is cheap to lease even when it is expensive to buy. A car that depreciates hard is the reverse: the sticker price may be modest and the lease painful. This is the single reason two cars at the same price can lease for very different money, and it has nothing to do with the dealer.
The money factor, and the number it is hiding
Leases quote a money factor rather than an interest rate. It is a small decimal, something like 0.00250, and it means almost nothing to most people at a glance, which is not entirely an accident.
Multiplying it by 2400 gives the equivalent annual rate, and doing that once turns an opaque figure into one that can be compared against a car loan. This page does it for you. Treat it as a comparison rather than a quoted rate: the multiplier is a trade convention, not a derivation, but it is the convention everyone in the business uses.
Cash at signing is not a deposit
Money put down on a lease lowers the payment and does not build anything. It is not equity and there is nothing to get back: if the car is written off or stolen early, that money is generally gone along with it, because the insurance settlement goes to the leasing company for the car's value rather than to you for what you paid in.
This is the standard argument for putting as little down on a lease as the deal allows and accepting the higher payment. It is a real argument, and it is the opposite of the advice that applies to buying.
What this page does not model
Mileage allowances and the per-mile charge for exceeding them, wear beyond what the agreement permits, the disposition fee at the end, gap cover, early termination, and the buyout price are all outside it. So is the question of whether leasing beats buying, which depends on how long you keep cars and what you do with the money in between.