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_monthsTotal 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_paymentTotal 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_amountVariables
| Variable | Description | Default |
|---|---|---|
vehicle_price | Vehicle Price(USD) | 35000 |
down_payment | Down Payment(USD) | 5000 |
annual_rate | Interest Rate (APR)(%) | 6.5 |
loan_months | Loan Term(months) | 60 |
loan_amount | Derived value= vehicle_price - down_payment | calculated |
monthly_rate | Derived value= annual_rate / 12 / 100 | calculated |
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.
- 01Loan amount = $35,000 - $5,000 = $30,000
- 02Monthly rate = 6.5% / 12 = 0.5417%
- 03Monthly payment = $30,000 x [0.005417 x 1.005417^60] / [1.005417^60 - 1] = $586.68
- 04Total paid = $586.68 x 60 + $5,000 = $40,200.80
- 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