# What car price can I afford?

Computes the most expensive car a monthly payment can buy, from the payment, loan rate and term, cash down, trade-in, sales tax and fees.

- Page: https://www.acalculator.org/finance/car-affordability-calculator
- JSON spec: https://www.acalculator.org/finance/car-affordability-calculator.json
- Version: 5a18f789110b

## Default answer

Example with the default inputs (Monthly payment you can afford $500.00, Cash down $3,000.00, Trade-in value $0.00, Interest rate (APR) 7%, Loan term (months) 60, Sales tax rate 0%, Dealer and registration fees $0.00): A payment of $500.00 a month for 60 months at 7%, with $3,000.00 down, buys a car of up to $28,251.00.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| payment | Monthly payment you can afford | The most you want to pay each month on the car loan. |
| down | Cash down | The cash you pay up front. |
| trade | Trade-in value | What the dealer pays for your current car. It also lowers the taxed price. |
| rate | Interest rate (APR) | The yearly interest rate on the car loan. |
| term | Loan term (months) | The number of monthly payments. |
| tax | Sales tax rate | Your state and local sales tax rate, charged on the price minus the trade-in. |
| fees | Dealer and registration fees | Title, registration, documentation and other fees, added to the loan. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| price | Car price you can afford | The highest price before tax and fees that the payment, cash down and trade-in cover. |
| loan | Loan amount | What the monthly payments repay: the price plus tax and fees, minus cash down and trade-in. |
| taxAmount | Sales tax | The sales tax rate times the price minus the trade-in. |
| interest | Total interest | All the monthly payments minus the loan amount. |
| totalCost | Total cost of the car | Price, tax, fees and interest: cash down plus trade-in plus all the payments. |

## Method

loan = payment × (1 − (1 + i)^−n) ÷ i with i = APR ÷ 12; price = trade-in + (loan + cash down − fees) ÷ (1 + sales tax rate).

## Assumptions

- A fixed-rate loan with equal monthly payments; sales tax and fees are added to the loan.
- Sales tax is charged on the price minus the trade-in, as the auto loan calculator assumes. States differ, so check your state’s rule.
- Insurance, fuel, maintenance and registration renewals are not included; budget for them on top of the payment.
- There is no answer when the fees are as large as, or larger than, the loan plus the cash down.

## Worked examples

1. payment = $450.00, down = $4,000.00, trade = $0.00, rate = 6.5%, term = 60, tax = 7%, fees = $600.00 gives price = $24,671.87, loan = $22,998.91, taxAmount = $1,727.03, interest = $4,001.09, totalCost = $31,000.00. Source: hand calculation in content.mdx: loan = 450 × (1 − 1.0054167⁻⁶⁰) ÷ 0.0054167 = 22,998.91; price = (22,998.91 + 4,000 − 600) ÷ 1.07 = 24,671.87.
2. payment = $400.00, down = $2,000.00, trade = $0.00, rate = 0%, term = 48, tax = 0%, fees = $0.00 gives price = $21,200.00, loan = $19,200.00, interest = $0.00. Source: hand calculation in content.mdx: at 0%, loan = 400 × 48 = 19,200; price = 19,200 + 2,000 = 21,200.
3. payment = $400.00, down = $2,000.00, trade = $0.00, rate = 0%, term = 48, tax = 6%, fees = $250.00 gives loan = $19,200.00, price = $19,764.15, taxAmount = $1,185.85. Source: hand calculation in content.mdx: loan = 400 × 48 = 19,200; price = (19,200 + 2,000 − 250) ÷ 1.06 = 19,764.15.
4. payment = $552.70, down = $6,000.00, trade = $0.00, rate = 5%, term = 48, tax = 0%, fees = $0.00 gives price = $30,000.00, loan = $24,000.00. Source: the reverse of the auto loan example ($30,000 price, $6,000 down, 5% for 48 months is $552.70 a month; amortized payment formula).
5. payment = $600.00, down = $2,000.00, trade = $5,000.00, rate = 7%, term = 72, tax = 6%, fees = $800.00 gives price = $39,332.70, taxAmount = $2,059.96, totalCost = $50,200.00. Source: hand calculation in content.mdx: loan 35,192.67; price = 5,000 + (35,192.67 + 2,000 − 800) ÷ 1.06 = 39,332.70; tax on 34,332.70.

## FAQ

### How much car can I afford?

Start from the monthly payment you can fit in your budget. The loan that payment repays depends on the rate and term: $450 a month for 60 months at 6.5% repays $22,998.91. Add your cash down, take off fees, and divide by (1 + sales tax rate) to get the price: with $4,000 down, $600 of fees and 7% tax, that is $24,671.87.

### Does a longer loan let me afford more car?

It raises the price a payment can cover, but you pay more interest in total, and a long loan can last longer than you want the car. Compare the total cost, not only the monthly payment.

### What costs should I include?

The CFPB suggests adding up the price, taxes, title and registration, and dealer fees, then taking off your down payment and trade-in. Also budget for insurance, fuel and maintenance, which this calculator does not include.

### How does a trade-in change what I can afford?

A trade-in adds its value to what you can spend, and in this calculator it also lowers the taxed amount, because sales tax is charged on the price minus the trade-in. Check your state's rule.

### How much of my income should go to a car payment?

There is no official limit. Lenders look at your debt-to-income ratio: all monthly debt payments, including the new car payment, divided by your gross monthly income. Use the debt-to-income ratio calculator to see how a payment changes it.

### What if I pay the tax and fees in cash?

Then more of each payment goes to the car. This calculator assumes tax and fees are added to the loan; if you pay them up front, add them to your cash down and set them to 0 here.

## Sources

- Consumer Financial Protection Bureau, How much can I afford to borrow for a car or auto loan? (price, taxes, title and fees add to the loan; down payment and trade-in reduce it; also budget for maintenance, gas and insurance). https://www.consumerfinance.gov/ask-cfpb/how-much-can-i-afford-to-borrow-for-a-car-or-auto-loan-en-751/
- Consumer Financial Protection Bureau, What is a debt-to-income ratio? https://www.consumerfinance.gov/ask-cfpb/what-is-a-debt-to-income-ratio-en-1791/
- Present value of a level payment (annuity), the inverse of the loan payment formula used by the auto loan calculator; derivation below.