Jackson Hayes is an expert in retail installment contracts and loan structuring, ensuring precise calculation of total auto financing costs and payment schedules.
Use the authoritative **Auto Loan Calculator** to determine your affordability. Simply enter any three variables—Principal Loan Amount, Annual Rate, Loan Term (Months), or Monthly Payment—to instantly solve for the remaining unknown value and budget for your new vehicle.
Auto Loan Calculator
Auto Loan Formula
The standard amortization formula for Monthly Payment (Q) is:
$$ Q = F \frac{i(1 + i)^n}{(1 + i)^n – 1} $$
Where $F$ is the Principal, $n$ is the Term in Months, and $i$ is the Monthly Rate (P / 1200).
Formula Source: BankrateFormula Variables
- F (Principal Loan Amount): The amount borrowed, typically the vehicle price minus down payment and trade-in.
- P (Annual Interest Rate): The nominal annual percentage rate (APR) of the loan (e.g., 5.9%).
- V (Loan Term): The length of time (in months) over which the loan must be repaid (e.g., 60 months).
- Q (Monthly Payment): The fixed amount paid each month towards principal and interest.
- i (Monthly Rate): P / 1200
- n (Total Payments): V (since V is already in months)
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What is an Auto Loan Calculation?
An auto loan calculation determines the fixed monthly payment required to pay off the cost of a vehicle over a specific term, accounting for the interest charged by the lender. Similar to a mortgage, auto loans use amortization, where the monthly payment covers both the accruing interest and a portion of the principal. The calculation is crucial for car buyers as it directly impacts their monthly budget and the total cost of ownership.
This calculator is a powerful tool because it allows for reverse engineering. If a dealership quotes you a high Monthly Payment (Q) for a 60-month term (V) at a known rate (P), you can solve for the maximum Principal (F) you should be borrowing. This helps shoppers negotiate the price of the vehicle itself. Conversely, if you have a budget cap for your payment, you can solve for the longest Term (V) required to meet that budget.
How to Calculate Loan Principal (Example)
Let’s find the maximum Principal (F) you can borrow if your budget allows for a \$450 monthly payment (Q) over 72 months (V) at a 4.5\% interest rate (P).
- Step 1: Calculate Monthly Rate ($\mathbf{i}$) and Total Payments ($\mathbf{n}$)
Monthly Rate ($i$) = $4.5\% / 12 / 100 = 0.00375$. Total Payments ($n$) = $72$.
- Step 2: Calculate the Present Value Factor (PVA Factor)
PVA Factor $= \frac{(1 + i)^n – 1}{i(1 + i)^n} \approx 64.195$.
- Step 3: Apply the Principal Formula ($\mathbf{F = Q \times \text{PVA Factor}}$)
Principal ($F$) = $\$450 \times 64.195$.
- Step 4: Determine the Maximum Principal
The calculation yields a maximum Principal (F) of approximately **\$28,887.75**.
Frequently Asked Questions (FAQ)
The Annual Percentage Rate (APR) is the true yearly cost of the loan, including the interest rate plus any fees. The interest rate is the base cost of borrowing. In simple amortization, they are often used interchangeably, but APR is legally the most accurate measure of cost.
Should I choose a longer term (e.g., 84 months)?Longer terms (V) result in lower monthly payments (Q) but significantly increase the total interest paid. You should only choose a longer term if the lower monthly payment is essential for your budget and you accept the higher long-term cost.
Does this calculator include trade-in or down payment?No. This calculator focuses only on the Principal Loan Amount (F). To get F, subtract your Down Payment and Trade-In value from the vehicle’s selling price before using the calculator.
What is negative equity (upside down)?Negative equity occurs when the amount you owe on the loan (Principal, F) is higher than the market value of the car. This often happens early in the loan term due to the rapid depreciation of new vehicles.