What This Calculator Does
The Monthly Payment to Affordable Price Calculator works backwards from a comfortable monthly payment to the maximum purchase price you can finance. Instead of guessing a price and discovering the payment is too high, you start with what you can actually pay each month and let the math reveal your budget. It is ideal for car shopping, but the same present-value formula applies to any fixed-rate installment loan.
How to Use It
Enter your desired monthly payment, the annual percentage rate (APR), the loan term in months, and any cash down payment or trade-in value. The calculator computes the largest loan that fits your payment, then adds your down payment and trade-in to show the maximum sticker price. It also reports the total of all payments and how much of that is interest.
The Formula Explained
The financed loan amount is the present value of an annuity: $$\text{Loan} = \text{PMT} \times \frac{1-(1+r)^{-n}}{r}$$, where \(r\) is the monthly interest rate (APR \(\div\) 12 \(\div\) 100) and \(n\) is the number of months. The affordable price adds your upfront cash: $$\text{Price} = \text{Loan} + \text{Down} - \text{TradeIn}$$. Total interest is simply all payments (\(\text{PMT} \times n\)) minus the loan amount.
Worked Example
Suppose you can pay $400/month, the APR is 6%, the term is 60 months, and you have $3,000 down. The monthly rate is \(0.06 \div 12 = 0.005\). $$\text{Loan} = 400 \times \frac{1 - 1.005^{-60}}{0.005} \approx \$20{,}690.24$$ $$\text{Affordable price} = 20{,}690.24 + 3{,}000 = \$23{,}690.24$$ Total of payments = \(400 \times 60 = \$24{,}000\), so total interest \(\approx\) $3,309.76.
FAQ
Does the price include taxes and fees? No. The result is the financeable amount; sales tax, registration and dealer fees should be budgeted separately.
What if my APR is 0%? With a 0% promotional rate, the loan equals payment \(\times\) term and there is no interest.
Why does a longer term raise the affordable price? More months means more total payments, so the same monthly amount finances a larger loan — but you also pay more interest overall.
