Auto Loan Calculator Formula

Understand the math behind the auto loan calculator. Each variable explained with a worked example.

Use the Auto Loan Calculator

Formulas Used

Monthly Payment

monthly_payment = monthly_rate > 0 ? loan_amount * monthly_rate * pow(1 + monthly_rate, loan_term_months) / (pow(1 + monthly_rate, loan_term_months) - 1) : loan_amount / loan_term_months

Total Amount Paid

total_paid = monthly_payment * loan_term_months

Total Interest

total_interest = total_paid - loan_amount

Variables

VariableDescriptionDefault
vehicle_priceVehicle Price(USD)35000
down_paymentDown Payment(USD)5000
trade_inTrade-In Value(USD)0
annual_rateInterest Rate(%)6.5
loan_term_monthsLoan Term(months)60
loan_amountDerived value= vehicle_price - down_payment - trade_incalculated
monthly_rateDerived value= annual_rate / 12 / 100calculated

How It Works

How Auto Loan Payments Work

An auto loan uses the same amortization formula as a mortgage, just with shorter terms and smaller amounts. You borrow the purchase price minus your down payment, and pay it back in equal monthly installments over 3-7 years. Each payment covers interest on the remaining balance plus a chunk of principal.

The Formula

Monthly Payment = P * [r(1+r)^n] / [(1+r)^n - 1]

  • P = Amount financed (vehicle price minus down payment minus trade-in value)
  • r = Monthly interest rate (APR / 12 / 100)
  • n = Number of monthly payments

    • When to Use This

    Before visiting a dealership. Know what your monthly payment will be at different price points so you negotiate on total price, not monthly payment. Dealers love to stretch the term to make any car look affordable. A $35,000 car at 6% for 72 months is $580/month. The same car for 48 months is $822/month, but you save $3,700 in interest.

    What Changes the Payment Most

    Loan term has the biggest impact on monthly payment. APR has the biggest impact on total cost. A 2% rate difference on a $30,000 loan over 60 months adds about $1,600 in total interest. Your credit score directly determines your rate: 750+ gets you 4-5%, 650-700 gets you 7-9%, below 600 can mean 12%+.

    The Hidden Cost of Long Terms

    A 72 or 84-month loan keeps payments low but creates a dangerous situation: you owe more than the car is worth for most of the loan. Cars depreciate 15-20% in year one. On a 72-month loan with minimal down payment, you could be $5,000-$8,000 underwater after two years. If you total the car or need to sell, you still owe the difference.

    Common Mistakes

  • Negotiating based on monthly payment instead of total price. The dealer can hit any monthly number by extending the term.
  • Forgetting taxes, registration, and dealer fees. These add 8-12% to the purchase price in most states and are often rolled into the loan.
  • Skipping pre-approval from your bank or credit union. Dealer financing is convenient but typically 1-2% higher than what you can get on your own.

    • Worked Example

    A $35,000 car with $5,000 down, no trade-in, 6.5% APR for 60 months.

    vehicle_price = 35000down_payment = 5000trade_in = 0annual_rate = 6.5loan_term_months = 60
    1. 01Loan amount = $35,000 - $5,000 = $30,000
    2. 02Monthly rate = 6.5% / 12 = 0.5417%
    3. 03Monthly payment = $30,000 × 0.005417 × 1.005417^60 / (1.005417^60 - 1)
    4. 04= $586.87
    5. 05Total paid = $586.87 × 60 = $35,212
    6. 06Total interest = $35,212 - $30,000 = $5,212

    Frequently Asked Questions

    What is a good interest rate for a car loan?

    Good rates vary by credit score. Borrowers with excellent credit (720+) typically qualify for 4-6% on new cars. Those with fair credit (620-679) may see rates of 10-16%. Used car loans typically carry rates 1-4% higher than new car loans.

    Should I choose a longer loan term?

    Longer terms mean lower monthly payments but significantly more total interest. A 72- or 84-month loan may also leave you "underwater" (owing more than the car is worth) since cars depreciate quickly.

    How much should I put down on a car?

    Experts recommend 20% down on a new car and 10% on a used car. A larger down payment reduces your loan amount, monthly payments, and total interest. It also protects you from being underwater if the car depreciates quickly.

    Is it better to finance through a dealer or bank?

    Compare both options. Banks and credit unions often offer better rates than dealer financing. However, dealers sometimes offer promotional 0% APR deals that are hard to beat. Always get pre-approved from a bank first so you have a baseline rate to compare.

    Learn More

    Guide

    How to Calculate Loan Amortization

    Learn how loan amortization works, how to build an amortization schedule, and how extra payments accelerate your payoff. Covers mortgages, auto loans, and personal loans.

    Ready to run the numbers?

    Open Auto Loan Calculator