Monthly car repayment formula

1. Calculate the monthly interest rate:
   $r = \frac{\text{Annual Interest Rate}}{12}$

2. Calculate the loan amount after deposit:
   $L = \text{Loan Amount} - \text{Deposit}$

3. Calculate the monthly installment without considering the residual:
   $M = \frac{L \times r}{1 - (1 + r)^{-\text{Months}}}$

4. Calculate the present value of the residual:
   $PV_{\text{residual}} = \frac{\text{Residual}}{(1 + r)^{\text{Months}}}$

5. Calculate the monthly installment considering the residual:
   $M_{\text{with residual}} = \frac{L - PV_{\text{residual}} \times r}{1 - (1 + r)^{-\text{Months}}}$

Where:

• $r$ is the monthly interest rate.
• $L$ is the loan amount after deducting the deposit.
• $M$ is the monthly installment without considering the residual.
• $PV_{\text{residual}}$ is the present value of the residual.
• $M_{\text{with residual}}$ is the monthly installment considering the residual.