Data Source and Methodology

AuthoritativeDataSource: Standard Loan Amortization Formula (Present Value of an Annuity).
Reference: Financial Mathematics & Compounding.

All calculations are based rigorously on this standard formula, which is used universally by financial institutions to determine loan payments.

The Formula Explained

The monthly payment ( $M$ ) is calculated using the standard auto loan amortization formula. First, we determine the Principal Loan Amount ( $P$ ):

$P = (\text{Price} + \text{Tax} + \text{Fees}) - (\text{Down Payment} + \text{Trade-in})$

Then, we use the principal ( $P$ ), the monthly interest rate ( $r$ ), and the number of payments ( $n$ ) to find the monthly payment ( $M$ ):

$M = P \frac{r(1+r)^n}{(1+r)^n - 1}$

Glossary of Variables

  • $M$ (Monthly Payment): The fixed amount you pay each month.
  • $P$ (Principal Loan Amount): The total amount of money you are borrowing after all costs and credits.
  • $r$ (Monthly Interest Rate): Your Annual Interest Rate (APR) divided by 12. (e.g., 6% APR is 0.005 per month).
  • $n$ (Number of Payments): The total loan term in months (e.g., a 5-year loan has $n=60$ ).

How It Works: A Step-by-Step Example

Let's use the default values to see how the calculation works:

  • Vehicle Price: $30,000
  • Sales Tax: 6% ($1,800)
  • Fees: $500
  • Down Payment: $5,000
  • Trade-in Value: $2,000
  • APR: 5%
  • Term: 60 months

1. Calculate Principal ( $P$ ):

First, find the total cost: $30,000 (Price) + $1,800 (Tax) + $500 (Fees) = $32,300.

Next, find the total credits: $5,000 (Down Payment) + $2,000 (Trade-in) = $7,000.

The principal to be financed is: $32,300 - $7,000 = $25,300 ( $P$ ).

2. Calculate Monthly Rate ( $r$ ) and Term ( $n$ ):

The monthly rate is 5% / 12 = 0.05 / 12 = 0.004167 ( $r$ ).

The term is 60 months ( $n$ ).

3. Apply the Formula:

$M = 25300 \frac{0.004167(1+0.004167)^{60}}{(1+0.004167)^{60} - 1}$

$M = 25300 \frac{0.004167(1.28335...)}{(1.28335...) - 1}$

$M = 25300 \frac{0.005347...}{0.28335...}$

$M = 25300 \times 0.01887...$

$M$ ≈ $477.42

Frequently Asked Questions (FAQ)

What is APR (Annual Percentage Rate)?

APR is the total cost of borrowing money expressed as a yearly percentage. It includes the interest rate plus any lender fees, making it a more accurate measure of a loan's cost than the interest rate alone.

How does a down payment affect my loan?

A larger down payment reduces your Principal Loan Amount ( $P$ ). This directly lowers your monthly payment and, more importantly, reduces the total amount of interest you'll pay over the life of the loan.

Is it better to get a longer loan term?

A longer term (e.g., 72 or 84 months) will give you a lower monthly payment, but you will pay significantly more in total interest. A shorter term (e.g., 48 or 60 months) has higher payments but saves you money and builds equity faster.

How is sales tax calculated on a trade-in?

This varies by state. Some states (like CA, MI, VA) tax the *full vehicle price* before applying the trade-in. Other states (like TX, FL, PA) are more favorable, only taxing the *difference* between the vehicle price and the trade-in value. This calculator assumes tax is applied to the full price, which is the more conservative estimate.

Can I pay off my auto loan early?

Most auto loans are not subject to pre-payment penalties, meaning you can pay extra each month or make lump-sum payments to pay it off early and save on interest. Always confirm with your lender that there are no pre-payment penalties.

Tool developed by Ugo Candido.
Content verified by the CalcDomain Editorial Board.

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