Auto Loan Calculator Formula
Understand the math behind the auto loan 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_term_months) / (pow(1 + monthly_rate, loan_term_months) - 1) : loan_amount / loan_term_monthsTotal Amount Paid
total_paid = monthly_payment * loan_term_monthsTotal Interest
total_interest = total_paid - loan_amountVariables
| Variable | Description | Default |
|---|---|---|
vehicle_price | Vehicle Price(USD) | 35000 |
down_payment | Down Payment(USD) | 5000 |
trade_in | Trade-In Value(USD) | 0 |
annual_rate | Interest Rate(%) | 6.5 |
loan_term_months | Loan Term(months) | 60 |
loan_amount | Derived value= vehicle_price - down_payment - trade_in | calculated |
monthly_rate | Derived value= annual_rate / 12 / 100 | calculated |
How It Works
How Auto Loan Payments Are Calculated
The monthly payment formula is the same amortization formula used for mortgages:
M = P × [r(1+r)^n] / [(1+r)^n - 1]
Where P = loan amount (price - down payment - trade-in), r = monthly rate, n = number of months.
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
- 01Loan amount = $35,000 - $5,000 = $30,000
- 02Monthly rate = 6.5% / 12 = 0.5417%
- 03Monthly payment = $30,000 × 0.005417 × 1.005417^60 / (1.005417^60 - 1)
- 04= $586.87
- 05Total paid = $586.87 × 60 = $35,212
- 06Total interest = $35,212 - $30,000 = $5,212
Ready to run the numbers?
Open Auto Loan Calculator