What this calculator does
This is a car affordability calculator that works backwards. Instead of starting with a car price and telling you the monthly payment, you start with the monthly payment you are comfortable with and it tells you the maximum car price you can afford. It also shows the loan amount you would need to borrow and a clear breakdown of how the price, sales tax, down payment and trade-in fit together. The sales-tax rules used here follow the US model.
How to use it
Enter the monthly payment you want to make, your sales-tax rate, any down payment and trade-in value, the loan term (in months or years), and the annual interest rate (APR). The tool returns the affordable car price and the car loan you would need. Adjust the payment up or down to instantly see how much more or less car you can afford.
The formula explained
First we convert your target monthly payment into a loan principal using the present value of an ordinary annuity: $$\text{Loan} = \text{PMT}\cdot\dfrac{1-(1+i)^{-n}}{i}$$ where \(i\) is the monthly interest rate (APR / 12) and \(n\) is the number of months. If the rate is 0%, the loan is simply \(\text{PMT}\times n\).
Next we turn that loan into a car price. The loan must cover the car price plus sales tax, minus your down payment and trade-in: \(\text{Loan} = \text{Price}\times(1+t)-\text{Down}-\text{Trade}\). Rearranging gives $$\text{Price} = \dfrac{\text{Loan} + \text{Down} + \text{Trade}}{1 + t}$$ where \(t\) is the sales-tax rate as a decimal. The sales-tax amount is then \(\text{Price}\times t\).
Assumption: this tool applies sales tax to the full car price. Some US states tax only the price minus the trade-in; if that applies to you, your actual tax will be a little lower.
Worked example
Suppose you want a $425 monthly payment, a 48-month term, 2.5% APR, 6% sales tax, $2,000 down and a $1,500 trade-in. The monthly rate is \(0.025 / 12 = 0.0020833\). The loan principal is $$425 \times \frac{1 - 1.0020833^{-48}}{0.0020833} \approx \$19{,}394.$$ The affordable price is $$\frac{19{,}394 + 2{,}000 + 1{,}500}{1.06} \approx \$21{,}598,$$ with sales tax of about $1,296.
FAQ
Does this include insurance or fees? No. It covers price, sales tax, financing, down payment and trade-in only. Budget separately for insurance, registration and dealer fees.
What if my down payment and trade-in already cover everything? If they exceed what you need to finance, the affordable price and loan are clamped to zero — meaning no loan is required.
Is the interest rate monthly or yearly? Enter the yearly APR; the calculator converts it to a monthly rate internally.
