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.
vehicle_price = 35000down_payment = 5000annual_rate = 6.5loan_months = 60
- 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
Ready to run the numbers?
Open Car Payment Calculator