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)
<!-- Total Interest Formula -->
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)
<!-- Loan Balance Formula -->
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