This Car Loan Payoff Calculator helps you determine the exact amount you'll need to pay to completely settle your car loan at any given point. It's a crucial tool for financial planning, whether you're considering selling your car, refinancing, or simply want to understand your loan's current standing.
How the Calculation Works
The calculator uses the standard formula for calculating the present value of an annuity, which represents the remaining balance of your loan. The formula is as follows:
PV = P * [1 – (1 + r)^-n] / r
Where:
PV is the Present Value (the total payoff amount).
P is the monthly payment amount.
r is the monthly interest rate (Annual Rate / 12).
n is the number of remaining payments.
Since the user typically doesn't know their exact monthly payment directly but rather the loan balance, annual interest rate, and remaining months, the calculator first derives the monthly payment using the loan amortization formula, and then uses that to calculate the payoff.
Step 1: Calculate the Monthly Payment (P)
If you don't have the monthly payment provided, we need to calculate it first. A common formula for calculating the monthly payment (M) for an amortizing loan is:
M = L * [r(1 + r)^n] / [(1 + r)^n – 1]
Where:
M is the monthly payment.
L is the loan principal amount (original loan amount, for calculation purposes here, we use the current balance as the starting point to derive what the monthly payment *should have been* to reach this balance over the remaining term).
r is the monthly interest rate (Annual Rate / 12).
n is the total number of payments (remaining months).
Step 2: Calculate the Total Payoff Amount (PV)
Once we have the derived monthly payment (M), we use it in the annuity formula (from the first section) to find the present value of the remaining payments, which is your total payoff amount.
Payoff Amount = M * [1 – (1 + r)^-n] / r
Note: If the interest rate is 0, the payoff amount is simply the remaining loan balance.
When to Use This Calculator
Selling Your Car: To know how much you owe the lender, which is essential for setting a sale price and completing the transaction.
Refinancing: To understand the exact amount needed to pay off the old loan before initiating a new one.
Early Payoff Strategy: To see the total financial commitment if you decide to pay off your loan early.
Financial Review: To keep track of your outstanding debts and plan your budget more effectively.
Example Calculation
Let's say you have a car loan with:
Current Loan Balance: $15,000
Annual Interest Rate: 4.5%
Number of Remaining Payments: 48 months
First, we calculate the monthly interest rate (r): 4.5% / 12 = 0.045 / 12 = 0.00375.
Next, we derive the monthly payment (M) using the loan amount ($15,000) as the principal for this calculation:
M = 15000 * [0.00375 * (1 + 0.00375)^48] / [(1 + 0.00375)^48 – 1]
M = 15000 * [0.00375 * (1.19668)] / [(1.19668) – 1]
M = 15000 * [0.00448755] / [0.19668]
M = 15000 * 0.022816
M ≈ $342.24
Now, we use this monthly payment ($342.24) to calculate the total payoff amount (PV) with 48 remaining payments:
The total payoff amount is approximately $15,000. This calculation shows the precise amount required to satisfy the loan obligations given the specified terms.
function calculatePayoff() {
var loanAmount = parseFloat(document.getElementById('loanAmount').value);
var interestRate = parseFloat(document.getElementById('interestRate').value);
var remainingMonths = parseInt(document.getElementById('remainingMonths').value);
var resultDiv = document.getElementById('result');
var resultValueDiv = document.getElementById('result-value');
if (isNaN(loanAmount) || isNaN(interestRate) || isNaN(remainingMonths) || loanAmount <= 0 || interestRate < 0 || remainingMonths <= 0) {
resultDiv.style.display = 'block';
resultValueDiv.innerHTML = "Please enter valid numbers.";
resultDiv.style.backgroundColor = '#f8d7da';
resultDiv.style.borderColor = '#f5c6cb';
resultValueDiv.style.color = '#721c24';
return;
}
var monthlyInterestRate = interestRate / 100 / 12;
var monthlyPayment = 0;
var payoffAmount = 0;
if (monthlyInterestRate === 0) {
// If interest rate is 0, payoff is simply the remaining balance
payoffAmount = loanAmount;
} else {
// Calculate the monthly payment first using the loan balance as the principal for this step
// This assumes the current balance is what would result from a loan of this principal, rate, and term.
// Formula: M = L * [r(1 + r)^n] / [(1 + r)^n – 1]
var principalForMCalculation = loanAmount; // Using current balance to derive the implied monthly payment
monthlyPayment = principalForMCalculation * (monthlyInterestRate * Math.pow(1 + monthlyInterestRate, remainingMonths)) / (Math.pow(1 + monthlyInterestRate, remainingMonths) – 1);
// Then calculate the present value (payoff amount) using the derived monthly payment
// Formula: PV = M * [1 – (1 + r)^-n] / r
payoffAmount = monthlyPayment * (1 – Math.pow(1 + monthlyInterestRate, -remainingMonths)) / monthlyInterestRate;
}
// Format the result to two decimal places
var formattedPayoff = payoffAmount.toFixed(2);
resultDiv.style.display = 'block';
resultValueDiv.innerHTML = "$" + formattedPayoff;
// Apply success styling
resultDiv.style.backgroundColor = '#d4edda';
resultDiv.style.borderColor = '#155724';
resultValueDiv.style.color = '#155724';
}