Auto Loan Calculator: Understanding Your Vehicle Financing

What is an Auto Loan?

An auto loan, also known as a car loan, is a type of installment loan used to finance the purchase of a vehicle. The borrower receives a lump sum to buy the car and agrees to repay the loan amount plus interest over a specified period, typically in monthly installments.

The Auto Loan Payment Formula

The formula used to calculate the monthly payment for an auto loan is:

\[P = L\frac{r(1+r)^n}{(1+r)^n-1}\]

Where:

• \(P\) = Monthly payment
• \(L\) = Loan amount
• \(r\) = Monthly interest rate (annual rate divided by 12)
• \(n\) = Total number of months in the loan term

Step-by-Step Calculation Process

1. Calculate the monthly interest rate: \[r = \frac{\text{Annual Interest Rate}}{12}\]
2. Apply the formula to calculate the monthly payment.
3. Calculate total payment: \[\text{Total Payment} = \text{Monthly Payment} \times \text{Number of Months}\]
4. Calculate total interest: \[\text{Total Interest} = \text{Total Payment} - \text{Loan Amount}\]

Example Calculation

Let's calculate the monthly payment for a $25,000 auto loan at 4.5% annual interest for 5 years:

1. \(r = \frac{4.5\%}{12} = 0.00375\)
2. \(P = 25000 \times \frac{0.00375(1+0.00375)^{60}}{(1+0.00375)^{60}-1} = 466.08\)
3. Total Payment = $466.08 × 60 = $27,964.80
4. Total Interest = $27,964.80 - $25,000 = $2,964.80

Visual Representation

The green portion represents the principal ($25,000), while the red portion shows the total interest ($2,964.80) over the life of the auto loan.