Car Payment Calculator Formula

Understand the math behind the car payment calculator. Each variable explained with a worked example.

Formulas Used

Monthly Payment

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

Total Amount Paid

total_paid = (monthly_rate > 0 ? loan_amount * monthly_rate * pow(1 + monthly_rate, loan_months) / (pow(1 + monthly_rate, loan_months) - 1) : loan_amount / loan_months) * loan_months + down_payment

Total Interest

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

Variables

VariableDescriptionDefault
vehicle_priceVehicle Price(USD)35000
down_paymentDown Payment(USD)5000
annual_rateInterest Rate (APR)(%)6.5
loan_monthsLoan Term(months)60
loan_amountDerived value= vehicle_price - down_paymentcalculated
monthly_rateDerived value= annual_rate / 12 / 100calculated

How It Works

How Car Payments Are Calculated

Car loans use the same amortization formula as any installment loan.

Formula

M = P x [r(1+r)^n] / [(1+r)^n - 1]

Where P = loan amount, r = monthly rate, n = number of months.

Worked Example

$35,000 vehicle, $5,000 down, 6.5% APR, 60-month term.

vehicle_price = 35000down_payment = 5000annual_rate = 6.5loan_months = 60
  1. 01Loan amount = $35,000 - $5,000 = $30,000
  2. 02Monthly rate = 6.5% / 12 = 0.5417%
  3. 03Monthly payment = $30,000 x [0.005417 x 1.005417^60] / [1.005417^60 - 1] = $586.68
  4. 04Total paid = $586.68 x 60 + $5,000 = $40,200.80
  5. 05Total interest = $586.68 x 60 - $30,000 = $5,200.80

Frequently Asked Questions

What is a good interest rate for a car loan?

For new cars with good credit: 3-6% APR. For used cars: 4-9%. Rates depend on your credit score, loan term, and the lender.

Is a longer or shorter loan term better?

Shorter terms have higher payments but less total interest. Longer terms lower monthly payments but cost more overall. Try to keep terms at 60 months or less.

How much should my down payment be?

At least 20% for new cars and 10% for used cars is recommended. A larger down payment reduces your loan amount and monthly payments.

Ready to run the numbers?

Open Car Payment Calculator