Car dealerships make the payment calculation feel like magic. It's not. The entire thing is one formula, and knowing it gives you power in any negotiation.
The Formula
M = P × [r(1+r)^n] / [(1+r)^n - 1]
Where:
- M = monthly payment
- P = principal (amount financed)
- r = monthly interest rate (APR / 12 / 100)
- n = number of months
That's it. That's the whole thing.
In JavaScript
function monthlyPayment(principal, apr, months) {
const r = apr / 100 / 12;
if (r === 0) return principal / months;
return principal * (r * Math.pow(1 + r, months)) / (Math.pow(1 + r, months) - 1);
}
// Example: $25,000 at 6.5% for 60 months
monthlyPayment(25000, 6.5, 60); // $489.15
Why This Matters
When a salesperson says "I can get you to $450 a month," you should be able to reverse-engineer what that actually means:
- At 6.5% for 60 months, $450/mo means you're financing about $22,990
- At 6.5% for 72 months, $450/mo means you're financing about $26,890
- At 9.9% for 84 months, $450/mo means you're financing about $28,100
See the game? Longer terms at higher rates make the payment look the same while you pay dramatically more in total interest.
$25,000 at 6.5% for 60 months: $4,349 in total interest
$25,000 at 9.9% for 84 months: $10,392 in total interest
Same car, same payment neighborhood, $6,000 difference.
The Real Power Move
Walk into a dealership knowing your credit score, your target APR, and your max total cost (not monthly payment). Negotiate the price first, then the rate.
I put a free calculator at simplylouie.com/loan-calculator — no signup, shows you payment + total interest + total cost side by side.
Part of the free tools at SimplyLouie. Free forever, no account needed.
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