New vs Used: The Depreciation Math That Decides It

“Buy used, it’s cheaper” gets repeated like a law of physics. It’s usually true — but not always, and not for the reason most people think. The savings don’t come from used cars being “cheaper.” They come from depreciation, and depreciation is a curve, not a flat discount. Once you put real numbers on it, the new-vs-used question stops being a slogan and becomes arithmetic you can settle in about thirty seconds.

Three numbers, fighting each other

Whether used wins comes down to three things pulling in different directions:

1. Depreciation — how much value each car loses while you own it. This almost always favors used.
2. Purchase discount — how much less the used car costs up front. The bigger the gap, the more used wins.
3. Running cost — maintenance and insurance. An older, out-of-warranty car usually costs more to keep running, which pulls back toward new.

The mistake is looking at only one of them. People who say “used is always cheaper” are staring at the purchase discount and ignoring the repair bills. People who say “I’d rather buy new and avoid headaches” are staring at maintenance and ignoring that depreciation dwarfs it. The right answer nets all three over the years you’ll actually own the car.

The depreciation curve, not a flat number

A car doesn’t lose value in a straight line. It falls off a cliff in year one — typically 15-25% — then declines more gently each year after. The clean way to model it is a declining balance:

resale value = price × (1 − rate)^years
depreciation = price − resale value

That year-one cliff isn’t about wear and tear. It’s the loss of new-car pricing power. The moment a car is titled it stops being new, and the new-car buyer pool won’t pay used prices for it — regardless of mileage. A one-year-old car with 4,000 miles has already taken essentially the full hit.

This is the entire case for buying used, stated precisely: a 2-3 year-old car has already absorbed the steepest part of the curve, so its depreciation over your ownership period is far flatter. You buy nearly the same usable car and let the first owner pay for the most expensive years.

Put it together: total cost over the hold

For each option, total cost over the years you keep it is just:

total = depreciation + (maintenance/yr × years) + (insurance/yr × years)

Compare the two totals and you have your answer. Divide the gap by the number of years and you get the single most useful figure in the whole exercise — the new premium per year: what insisting on new actually costs you annually, after the used car’s higher maintenance is already subtracted.

A worked example

Take a $38,000 new car against a comparable 3-year-old used one at $26,000, held for six years.

• New: depreciates ~17%/yr, $600/yr maintenance (warranty), $1,700/yr insurance.
• Used: depreciates ~12%/yr, $1,100/yr maintenance (out of warranty), $1,400/yr insurance.

Running the curve:

• New resale ≈ 38,000 × 0.83⁶ ≈ $13,200 → depreciation ≈ $24,800.
• Used resale ≈ 26,000 × 0.88⁶ ≈ $11,600 → depreciation ≈ $14,400.
• New total ≈ 24,800 + 3,600 + 10,200 ≈ $38,600.
• Used total ≈ 14,400 + 6,600 + 8,400 ≈ $29,400.

Used wins by about $9,000 over six years — roughly $1,500 a year — even though it costs $500 more per year to maintain. Notice what’s carrying the result: the $10,000-plus depreciation difference, not the maintenance line. The repair bills are real, but they’re a rounding error next to the cliff the new buyer paid for.

When new actually wins

It’s not always used. The math flips toward new when:

• The used premium is small. In a tight used market, a 3-year-old car might cost $34,000 against a $38,000 new one. A $4,000 discount doesn’t buy much margin, and if the used car also needs $2,500/yr in maintenance, new can come out ahead. The calculator will tell you when the discount isn’t doing enough work.
• You keep cars a very long time. Hold a car 12 years and the year-one cliff amortizes across more than a decade — the per-year penalty for buying new shrinks.
• A subsidized new-car offer narrows the gap. Manufacturer 0% APR or a fat rebate can close enough of the price gap to matter. (Financing isn’t in this calculator — compare loans separately with the auto loan calculator, since used APRs run 1-3 points higher.)
• Warranty and zero early-repair risk are worth a premium to you. That’s a legitimate preference; the calculator just tells you its annual price so you’re choosing it with eyes open.

Certified pre-owned: the middle lane

CPO sits between the two. You pay more than a private-party used car, but you get a manufacturer-backed warranty and an inspection — which knocks down exactly the repair-risk and maintenance cost that normally count against used. Model a CPO car with its higher purchase price but a lower maintenance figure, closer to the new-car number for the warranty period. It often lands neatly between new and private-party used on total cost, which is the whole point of it.

What the math leaves out

• Mileage and condition. Resale here is time-based; a high-mileage used car depreciates faster than the curve shows.
• Reliability spread. The used maintenance number is an average. A specific older car can be far better or worse — which is what a pre-purchase inspection and a CPO warranty are buying down.
• Fuel and the rest of ownership. This isolates the new-vs-used decision. For the complete picture, run it through True Cost of Ownership.

The one-paragraph version

New vs used isn’t decided by sticker price — it’s decided by depreciation. A new car loses 15-25% in year one to the loss of new-car pricing power, so a 2-3 year-old car that already ate that cliff usually costs thousands less to own even after its higher maintenance. Net depreciation, purchase discount, and running cost over the years you’ll actually keep the car, and read the new premium per year. If it’s large, used is doing real work for you; if it’s small, new’s warranty might be worth it. Settle it with the new vs used calculator.

Related calculators

• New vs Used Calculator — net the three numbers for your own car.
• Car Depreciation — the value curve that drives the whole decision.
• True Cost of Ownership — depreciation in the context of every cost.
• Auto Loan — used APRs run higher; price the financing on each option.

AutoMath is an educational tool, not financial advice. Calibrate the depreciation rates with real used-price data for your specific vehicle.