Auto Loan Formulas

1. Monthly Payment Formula

The formula to calculate the monthly payment (M) for an auto loan is:

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

Where:

• M = Monthly Payment
• P = Loan Amount (Principal)
• r = Monthly Interest Rate (Annual Rate / 12)
• n = Number of Payments (Loan Term in Months)

2. Total Interest Formula

The formula to calculate the total interest paid over the life of the loan is:

\[ \text{Total Interest} = (M \cdot n) - P \]

Where:

• M = Monthly Payment
• n = Number of Payments (Loan Term in Months)
• P = Loan Amount (Principal)

3. Loan Balance Formula

The formula to calculate the remaining loan balance after a certain number of payments is:

\[ B = P \cdot \left( \frac{(1 + r)^n - (1 + r)^t}{(1 + r)^n - 1} \right) \]

Where:

• B = Remaining Loan Balance
• P = Loan Amount (Principal)
• r = Monthly Interest Rate (Annual Rate / 12)
• n = Total Number of Payments
• t = Number of Payments Made So Far