How this model works
Every option is one stream of payments plus whatever the car is worth at the end. The idea that makes them comparable is opportunity cost: money you do not hand to a dealer stays invested, so a dollar paid in month t costs you the dollar and the growth it never earned.
net cost = SUM outflow(t) x (1 + r)^(N - t)
- what the car is worth at the horizon
+ anything still owed
Lower wins. Your income is the same whichever way you pay, so it cancels out and is never modelled. Maintenance, insurance, registration and fees are outflows too, so they lose their market growth on exactly the same footing as the payment.
The last number the chart shows is the number in the table. They are the same calculation, measured at every month in between.
Is a lease ever the cheaper way?
A lease is a way of buying the steepest part of the depreciation curve and nothing else. You pay the difference between what the car costs today and what the lessor thinks it will be worth at the end, plus interest on the whole value in the meantime.
That makes the comparison turn on how long you keep the car. Over one lease term, leasing is often within a few hundred dollars of buying, because you have paid for the same depreciation either way. Keep re-leasing and you are buying the steep part of the curve again and again, and never own anything at the end of it. Over eight years that is the largest gap on this page — and it is not close.
The lease's real advantage in this model is quieter: maintenance tracks the age of the car, not the calendar, and a re-leased car is always nearly new. That is worth thousands over a long horizon. It is just not worth as much as the depreciation it repurchases.
Buying used, and buying private
The first year is the most expensive year a car ever has. Set the age of the car you buy above zero and the purchase options skip it: the model runs the same depreciation curve from the car's real age, so a three-year-old car loses a much smaller share of what you paid for it over the years you own it. That is the entire financial case for buying used, and it is a large one.
It is not free. A car past its warranty carries the full maintenance bill from the day you buy it, and maintenance in this model tracks the car's age, so an older car costs more to run every month you own it. The calculator charges both effects and shows you the net.
Buying from a private seller removes the dealer's paperwork fee and nothing else. Sales tax is usually still collected when you register the car, which is why it stays on by default — switch it off only if you have checked your own state. The saving is real but modest: it is the fee, plus the market growth of the fee, and it will not decide anything on its own.
One honest caveat, which the calculator repeats when it applies: a lease starts with a new car. Once you set an age above zero you are no longer comparing two ways to get the same car — you are comparing leasing new against owning something older, which is a real question but a different one. Part of the gap you see is the cheaper car, not the cleverer deal.
When financing beats paying cash
Compare the loan APR against the market return. Borrow at 3% while your money compounds at 7% and the loan wins; borrow at 9% against the same 7% and it loses. The crossing is close to the APR itself, and the calculator solves for it: the verdict tells you the market return at which the ranking flips.
Two things move that crossing off the APR. Interest is charged on a balance that falls every month, while your investments compound on the whole balance the whole time — which favours the loan. Taxes on investment gains cut the return you are actually comparing against — which favours cash. Set the tax drag and see.
A 0% promotional rate is the clean case: financing at 0% strictly beats paying cash, because the money stays invested at no cost. If the 0% is only available at a higher price, put that higher price in and compare properly.
The residual decides everything about a lease
The residual is what the lessor expects the car to be worth when you hand it back. It sets the payment: a high residual means less depreciation to pay for, so the monthly is lower. And it sets whether buying the car out at the end is a bargain or a mistake, because the buyout price is the residual.
Those two effects pull against each other, which is why the model shows the residual next to the car's projected market value on the same day. If the residual is well above market, the lease was cheap and the buyout is bad — hand the keys back. If it is below market, the lease was expensive and the buyout is the deal. A lease with a rich residual is not a generous lease; it is a lease that has priced the buyout out of your reach.
Mileage: the bill that arrives at the end
A lease meters your driving. Every mile over the allowance is charged at the end, at a rate set in the contract, and it is the one lease cost that does not appear in the monthly payment you were quoted.
Owning does not escape it — excess miles come off the resale value instead — but the two are charged differently. The lease bill is fixed per mile and payable in cash on a specific day; the ownership cost is a softer haircut on a number you only find out when you sell. The model charges both.
Negative equity, and what gap insurance is for
A new car loses value faster than a loan pays down, so for the first couple of years the balance can exceed what the car is worth. Total the car in that window and the insurer pays its value, not your loan: the difference is a debt on a car you no longer have. That gap is what gap insurance covers, and the calculator draws it — how deep it goes, and the month it closes.
A larger down payment closes it sooner. It is also the most expensive money in the deal by the opportunity-cost measure above. That tension is real, and it is a risk question rather than an arithmetic one: the model prices the cost, not your tolerance for the risk.
What this model leaves out
Fuel and tyres, which are near enough identical across the options and so cannot change the ranking. Mid-lease exits and lease transfers. Gap insurance premiums. Business use, depreciation deductions and EV credits. Lot-level capital-gains tax — investment tax is modelled as a flat drag on the return instead.
It also has nothing to say about the part that is not arithmetic: whether you want a new car every three years, and what that is worth to you. The number this page produces is the price of that preference, not an argument against it.