01
The Reverse Loan Formula (Present Value of an Annuity)
This calculator works backward from "how much car can I afford" based on a monthly payment. With monthly rate r = APR ÷ 100 ÷ 12 and loan term n (months), the loan principal you can afford is derived from the present-value-of-an-annuity formula.
Principal = PMT × (1 − (1 + r)⁻ⁿ) ÷ r
When the APR is 0% (a promotional 0% financing offer), we avoid dividing by zero and simply use Principal = PMT × n. Adding the down payment and trade-in value to the principal gives the affordable car price, and subtracting the principal from the total paid (PMT × n) gives the total interest.
Principal = PMT × (1 − (1 + r)⁻ⁿ) ÷ r
When the APR is 0% (a promotional 0% financing offer), we avoid dividing by zero and simply use Principal = PMT × n. Adding the down payment and trade-in value to the principal gives the affordable car price, and subtracting the principal from the total paid (PMT × n) gives the total interest.