Find the hidden APR based on your quoted monthly payment.
Include sales tax, title, doc fees.
Total amount reducing the loan balance.
The payment amount the dealer offered.
Financing Analysis
Effective APR:0.00%
Amount Financed:$0.00
Total Interest Cost:$0.00
Total Payments:$0.00
Understanding Your Auto Financing Rate
When purchasing a vehicle, dealerships often focus negotiations on the "monthly payment" rather than the actual price of the car or the interest rate. This sales tactic, often called "payment packing," can obscure the true cost of borrowing. The Auto Financing Rate Calculator is designed to reverse-engineer the math. By inputting the vehicle price, your upfront contribution (cash or trade-in), and the quoted monthly payment, this tool calculates the Effective Annual Percentage Rate (APR) you are actually being charged.
Why Calculate the Implied Rate?
Knowing the implied APR gives you leverage. If a dealer quotes you a monthly payment of $450 for 60 months on a $20,000 balance, it might sound affordable. However, plugging these numbers into the calculator reveals the interest rate used to arrive at that number. If the calculated APR is higher than market averages or pre-approved rates you've received from a credit union, you know there is room for negotiation.
Key Inputs Explained
Vehicle Selling Price: The negotiated price of the car before any financing charges.
Taxes & Dealer Fees: Non-negotiable government fees (sales tax, registration) and dealer documentation fees that are rolled into the loan.
Cash / Trade-in Equity: This replaces the traditional "Down Payment". It is the sum of any cash you put down plus the value of your trade-in vehicle minus any existing lien payoff.
Financing Term: The duration of the contract in months (commonly 36, 48, 60, 72, or 84).
Quoted Monthly Payment: The specific dollar amount the lender or dealer says you will pay each month.
How the Calculation Works
Most auto loans are simple interest amortized loans. While standard calculators ask for an interest rate to tell you the payment, this tool uses an iterative numerical method to solve for the interest rate variable based on the payment you provide. This "reverse calculation" ensures transparency in your financial agreement.
Interpreting the Results
Effective APR: This is the annualized cost of credit. Compare this number against current auto loan rates. Total Interest Cost: The total amount of money paid solely for the privilege of borrowing. Amount Financed: The net amount you are borrowing after taxes are added and your upfront equity is subtracted.
function calculateAutoAPR() {
// 1. Get Inputs by ID
var priceInput = document.getElementById("vehiclePrice");
var feesInput = document.getElementById("feesAndTaxes");
var equityInput = document.getElementById("upfrontEquity");
var termInput = document.getElementById("loanTerm");
var paymentInput = document.getElementById("quotedPayment");
// 2. Parse values
var price = parseFloat(priceInput.value) || 0;
var fees = parseFloat(feesInput.value) || 0;
var equity = parseFloat(equityInput.value) || 0;
var term = parseInt(termInput.value) || 0;
var payment = parseFloat(paymentInput.value) || 0;
// 3. Elements for display
var resultDiv = document.getElementById("resultsSection");
var errorDiv = document.getElementById("errorDisplay");
var resApr = document.getElementById("resApr");
var resPrincipal = document.getElementById("resPrincipal");
var resInterest = document.getElementById("resInterest");
var resTotalPayments = document.getElementById("resTotalPayments");
// 4. Validation
errorDiv.style.display = "none";
resultDiv.style.display = "none";
if (price <= 0 || term <= 0 || payment <= 0) {
errorDiv.innerHTML = "Please enter valid positive numbers for Price, Term, and Payment.";
errorDiv.style.display = "block";
return;
}
// 5. Calculate Principal (Amount Financed)
var principal = price + fees – equity;
if (principal <= 0) {
errorDiv.innerHTML = "Your upfront equity covers the entire cost. No financing required.";
errorDiv.style.display = "block";
return;
}
// Check if payment covers principal
var totalScheduled = payment * term;
if (totalScheduled < principal) {
errorDiv.innerHTML = "The total payments (" + formatCurrency(totalScheduled) + ") are less than the amount financed (" + formatCurrency(principal) + "). This is mathematically impossible for a loan.";
errorDiv.style.display = "block";
return;
}
// 6. Calculate Rate (Binary Search for APR)
// Formula: P = (r * PV) / (1 – (1+r)^-n)
// We need to find 'r' (monthly rate)
var minRate = 0.0;
var maxRate = 1.0; // 100% monthly rate (extreme upper bound)
var tolerance = 0.0000001;
var foundRate = 0;
// Binary search loop (100 iterations is plenty for precision)
for (var i = 0; i < 100; i++) {
var midRate = (minRate + maxRate) / 2;
// Avoid division by zero if rate is 0
var calculatedPayment = 0;
if (midRate < 0.00000001) {
calculatedPayment = principal / term;
} else {
calculatedPayment = (principal * midRate) / (1 – Math.pow(1 + midRate, -term));
}
if (Math.abs(calculatedPayment – payment) payment) {
maxRate = midRate;
} else {
minRate = midRate;
}
foundRate = midRate;
}
// 7. Process Results
var monthlyRate = foundRate;
var annualRate = monthlyRate * 12 * 100; // Convert to percentage
var totalInterest = totalScheduled – principal;
// 8. Update DOM
resApr.innerText = annualRate.toFixed(2) + "%";
resPrincipal.innerText = formatCurrency(principal);
resInterest.innerText = formatCurrency(totalInterest);
resTotalPayments.innerText = formatCurrency(totalScheduled);
resultDiv.style.display = "block";
}
function formatCurrency(num) {
return "$" + num.toFixed(2).replace(/\d(?=(\d{3})+\.)/g, '$&,');
}