Formula
The financed amount is the present value of the payment. The price adds the down payment:
price = payment × (1 − (1 + r)^−months) / r + down payment
When the rate is zero, the financed amount is the payment times the months. Sales tax is not added. The car loan page goes the other way and includes tax.
Assumptions
- The payment is principal and interest only.
- The rate is fixed and compounded monthly.
- The down payment is cash, not a trade-in.
Worked example
A $450 payment at 6.5% for 60 months, plus $2,000 down, reaches a vehicle price of $24,998.91.
Input definitions
- Monthly payment
- The principal-and-interest payment you want to stay within.
- Vehicle price
- The financed amount plus the down payment. Tax is not inside it.
Limitations
This is an estimate, not a loan offer, a lease quote, or tax advice. A lender can add fees, and sales-tax rules differ by place. The currency control changes the symbol only.
Questions
Why is there no sales tax?
Tax would shrink the price that fits the payment, and the rate differs by place. Subtract tax yourself, or start from a known price on the car loan page.
What does a zero rate do?
The financed amount is the payment multiplied by the number of months.