Auto & Vehicle Financing, Explained

Buying or leasing a vehicle is one of the largest transactions most people make, and the numbers are easy to lose track of once a salesperson starts moving figures around. This guide explains how a car payment is actually built, how the pieces — tax, trade-in, fees, rebates — fit together, and how to compare a lease against a loan or a rebate against a low interest rate. The goal is to help you understand the math behind every BedrockCalc auto calculator, not to give you personalized advice.

How a car payment is built

Every financed vehicle starts with an amount you are borrowing. That figure is assembled from a short list of additions and subtractions:

• Vehicle price — the negotiated sale price, not the sticker (MSRP).
• Minus your trade-in — the value the dealer credits for your old vehicle.
• Plus sales tax — calculated on the taxable amount (more below).
• Plus fees — documentation, title, registration and dealer fees.
• Minus your down payment — cash you pay up front.
• Minus any rebate — a manufacturer incentive that lowers the amount financed.
• Plus any amount still owed on the trade-in — negative equity rolled into the new loan.

Put simply, the amount financed is: price − trade-in + tax + fees − down − rebate + amount owed. That total becomes the loan principal, which the payment formula turns into a monthly figure.

The loan-payment formula

Once you know the principal, the term and the interest rate, the monthly payment is fixed. The standard amortized-loan formula is:

M = P·r(1+r)^n / ((1+r)^n − 1)

• P is the amount financed (the principal).
• r is the monthly interest rate — the annual APR divided by 12.
• n is the number of monthly payments (years × 12).
• M is the monthly payment.

The same engine powers the Auto Loan and Boat Loan calculators; boats simply tend to use longer terms — 15 or even 20 years is common — which lowers the monthly payment but raises total interest.

How US sales tax on cars works

Sales tax on a vehicle is charged by your state and locality, and the rate varies widely. BedrockCalc does not keep 50-state tax tables — you enter the rate that applies to you, and the calculator does the arithmetic.

• In most states, the taxable amount is the price minus your trade-in. Trading in a $10,000 car against a $30,000 purchase means you are often taxed on $20,000, not $30,000.
• A few states tax the full purchase price regardless of trade-in. Check your state’s rule before relying on the trade-in credit.
• Rebates may or may not be taxed first depending on the state — some tax the pre-rebate price.
• The formula the Auto Loan calculator uses is straightforward: taxable = price − trade-in, then sales tax = taxable × your rate.

Negative equity: owing more than the trade is worth

If you still owe money on your current vehicle and it is worth less than that balance, you have negative equity — often called being “upside down.”

• The unpaid balance above the trade-in value is the amount owed, and dealers typically roll it into the new loan.
• Rolling it in increases the principal, so you pay interest on the old debt again.
• This is one of the fastest ways to end up upside down on the next car, too.
• If you can, paying off negative equity in cash rather than financing it keeps the new loan smaller.

Should you put money down?

A down payment is not required on many loans, but it changes the math in your favor.

• It lowers the principal, so both the monthly payment and total interest drop.
• It offsets fast depreciation — new vehicles lose value quickly, and a down payment helps you avoid being upside down early in the loan.
• It can improve your rate, since a larger down payment reduces the lender’s risk.
• There is no universal “right” amount; more down means less borrowed, but keep enough cash for emergencies.

Loan versus lease

A loan buys the vehicle; a lease rents it for a set term. The trade-offs are different:

• A loan builds ownership. Payments are higher, but the vehicle is yours once it is paid off.
• A lease covers only the vehicle’s depreciation during the term, so payments are usually lower — but you own nothing at the end.
• Leases cap your mileage and charge for wear; loans do not.
• If you drive a lot or keep cars for years, buying usually costs less overall. If you like a new vehicle every few years and drive modestly, a lease can be competitive.

How a lease payment is calculated

A lease payment has two parts plus tax, and understanding them is the best defense against a confusing dealer worksheet.

• Capitalized cost (cap cost) — the negotiated price of the vehicle, the lease equivalent of the sale price.
• Residual value — what the vehicle is projected to be worth at lease end, usually quoted as a percentage of MSRP.
• Depreciation fee — (cap cost − residual) / term. This is the value you use up.
• Finance fee — (cap cost + residual) × money factor. This is the lease’s interest cost.
• Monthly payment — depreciation fee + finance fee + tax on your local rate.

Money factor and the APR conversion

Leases quote interest as a small decimal called the money factor rather than an APR, which makes rates hard to compare. The conversion is simple:

• Money factor = APR / 2400, so an APR of 6% is a money factor of 0.0025.
• To go the other way: APR = money factor × 2400.
• A money factor of 0.00125 is a 3% APR; 0.00375 is 9%. Convert before you judge whether a lease rate is fair.

Cash rebate versus low-interest financing

Manufacturers often make you choose one incentive or the other: a cash rebate that lowers the price, or a low (sometimes 0%) APR. There is no shortcut rule — you compare total cost.

• Option A: low or 0% APR on the full price. Little or no interest, but you finance the larger amount.
• Option B: take the rebate, finance at a normal market rate. A smaller principal, but real interest on top.
• Calculate the monthly payment for each, multiply by the number of payments, and compare total cost.

A worked example

Suppose a truck costs $35,000 on a 60-month term, and the automaker offers either 0% APR or a $3,000 rebate with 6% APR financing.

• Option A (0%, full price): $35,000 ÷ 60 = about $583/month, or $35,000 total.
• Option B ($3,000 rebate, 6%): finance $32,000 at 6% over 60 months. Using the loan formula, the payment is about $619/month, or roughly $37,120 total.
• Here the 0% financing wins by about $2,100. But if the rebate were larger or the term shorter, the rebate could win — which is exactly why you run both.

Putting the pieces together

A second short example ties the buying side together. Say you buy a $28,000 car, trade in a vehicle worth $6,000 (on which you still owe $2,000), put $2,000 down, pay a 7% sales-tax rate and $500 in fees:

• Taxable amount: $28,000 − $6,000 = $22,000.
• Sales tax: $22,000 × 7% = $1,540.
• Amount financed: $28,000 − $6,000 + $1,540 + $500 − $2,000 + $2,000 = $24,040.
• At 6% APR over 60 months, that is roughly $465 per month.

Run your own numbers through the calculators below, and remember that the sales-tax rate is always something you supply — BedrockCalc does the arithmetic, not the tax lookup. None of this is financial advice; it is the math you can check for yourself before you sign.