What this calculator works out, and what you need
This page answers the two questions that come up when financing a vehicle, in four tabs. From the rate to the payment: if you know the interest, it works out what you would pay. From the payment to the rate: if you already have an offer, it works out what interest is buried in it. The numbers you type carry over from one tab to the next.
Car payment needs the vehicle price, down payment, term and annual rate, plus sales tax and fees if you have them. It returns the monthly payment, the amount financed, the total interest, the total of payments and the total out of pocket, with a chart of principal against interest.
Find the rate needs four numbers — total price, down payment, term in months and monthly payment. It returns the monthly, nominal annual and effective annual rates, plus the amount financed, the total of payments, the total interest and the total outlay.
Compare car payments needs three — car price, down payment and annual rate, saying whether that rate is nominal or effective. It returns a table with the monthly payment, total interest, total of payments and total with down payment for 36, 48, 60, 72 and 84 months, plus any custom term you add.
Check a lease takes the numbers on a lease quote and works out the money factor, the equivalent APR and the real total cost of the lease.
How to use each calculator
Find the rate in an offer you already have
Open the «Find the rate» tab, type the price and down payment exactly as the offer states them, the term in months and the monthly payment being proposed, then press «Calculate rate». The estimated effective annual rate appears at the top, with the full breakdown below it.
Compare payments on a car loan
Open the «Compare car payments» tab, type the car price, the down payment and the annual rate, and choose whether that rate is nominal or effective. For a term that is not in the table, type it in months under «Custom term». Press «Compare payments» and pick any row to see its summary.
The currency selector changes how amounts are formatted; it does not convert between currencies.
What each number means
- Down payment
- The money you hand over up front, which is not financed. It lowers the amount borrowed but does not change the rate you are charged.
- Amount financed
- The total price minus the down payment: the money actually lent to you, and the balance interest runs on.
- Monthly payment
- The fixed amount due each month. Part of it is interest and part repays the principal; early on the first weighs more, later the second.
- Total interest
- The sum of every payment minus the amount financed: what the loan costs you, before any extra charges.
- Total of payments and total outlay
- The total of payments is the monthly payment times the number of months. The total outlay adds the down payment: everything that leaves your pocket.
- Monthly rate
- The rate applied to the outstanding balance in each payment.
- Nominal annual rate
- The monthly rate multiplied by twelve, without compounding. It is the usual way financing offers quote interest.
- Effective annual rate
- That same monthly rate compounded over twelve months. It is always higher than the nominal rate when there is interest, because it reflects interest building on itself. Note it is not the APR a regulator requires: that one also folds in fees and insurance, which this calculator knows nothing about.
How the term changes the cost
A longer term spreads the same principal over more payments: you pay less each month, but you pay for longer, so the total interest goes up. This table compares three terms assuming the same amount financed and the same fixed rate: $16,000 at 12 % nominal annual.
| Term | Monthly payment | Total interest | Total of payments |
|---|---|---|---|
| 3 years (36 months) | $531.43 | $3,131.44 | $19,131.44 |
| 5 years (60 months) | $355.91 | $5,354.67 | $21,354.67 |
| 7 years (84 months) | $282.44 | $7,725.27 | $23,725.27 |
Going from three years to seven nearly halves the payment and multiplies the interest by about 2.5. Neither figure decides on its own: the payment rules your monthly budget, the total interest rules what you end up handing over.
The zero-interest case
At a 0 % rate the payment is simply the principal divided by the number of months, and total interest is zero on every term. The term then changes only the size of the payment, not the cost. The calculator detects this and says so on screen.
Formulas and assumptions
With P as the amount financed, n as the number of months, r as the monthly rate in decimal form and i as the annual rate in decimal form:
- Amount financed
P = price − down payment- Monthly payment
Payment = P × r ÷ [1 − (1 + r)^−n]- Monthly payment at 0 %
Payment = P ÷ n- Total of payments
Total = Payment × n- Total interest
Interest = Total − P- Total outlay
Outlay = down payment + Total- Nominal → monthly
r = i ÷ 12- Effective → monthly
r = (1 + i)^(1/12) − 1- Monthly → nominal annual
i = r × 12- Monthly → effective annual
i = (1 + r)^12 − 1
These hold under one set of assumptions: a fixed rate for the whole loan, equal payments, payments made at the end of each month, twelve payments a year, no grace period and no balloon payment.
Worked example: a $20,000 car over five years
Vehicle price $20,000, down payment $4,000, rate 12 % nominal annual, term 60 months.
- Amount financed: 20,000 − 4,000 = 16,000.
- Monthly rate: 12 % ÷ 12 = 1.000 % (0.01 in decimal).
- Payment: 16,000 × 0.01 ÷ [1 − 1.01^−60] = 355.91.
- Total of payments: 355.91 × 60 = 21,354.67.
- Total interest: 21,354.67 − 16,000 = 5,354.67.
- Total outlay: 4,000 + 21,354.67 = 25,354.67.
- Effective annual rate: 1.01^12 − 1 = 12.68 %.
It checks out in both directions: typing price 20,000, down payment 4,000, 60 months and a 355.91 payment into «Find the rate» returns 1.000 % monthly and 12.00 % nominal annual, which is the rate we started from.
In that reverse check the totals come out seven cents lower — 21,354.60 instead of 21,354.67 — because the exact payment is 355.9111… and typing it rounded drops the fraction. That is precisely the rounding effect described below, and the same one you will see between this estimate and a lender's amortization schedule.
How this page calculates
Payments. It uses the standard amortization formula for equal payments in arrears, shown above. It is the same one behind the amortization schedule of a fixed-rate loan.
Implied rate. There is no closed form for the rate given the payment, so it is solved numerically by bisection: the tool searches for the monthly rate that makes the present value of every payment equal the amount financed, narrowing the interval until it converges. When the payments do not add up to the principal, it says so instead of showing a negative rate.
Rate conversion and rounding. The annual rate is converted to monthly before anything is calculated — simply if it is nominal, with compounding if it is effective. Every intermediate step keeps full precision; rounding happens only when results are displayed, so small differences against your lender's schedule are expected.
What is left out. The estimates exclude insurance, origination fees, administrative costs and balloon payments, and assume no early repayment. Sales tax and title or registration fees are counted only when you enter them. This is not a loan offer and not financial advice: it is arithmetic on the numbers you type.
Everything is calculated in your browser. Your numbers are not sent anywhere, not stored, and never appear in the page address.
Frequently asked questions
How do you work out a car's monthly payment?
Subtract the down payment from the price to get the amount financed, turn the annual rate into a monthly rate, and apply the equal-payment formula. In the «Compare car payments» mode you only need to type the car price, the down payment and the annual rate: the payment for each term is calculated in the table.
How does the down payment affect the monthly payment?
The down payment does not change the rate, but it does change the balance interest runs on. On a $20,000 car at 12 % nominal annual over 60 months, a $2,000 down payment leaves a payment of $400.40, while $6,000 brings it down to $311.42; total interest falls from $6,024.00 to $4,685.34.
What is the difference between financing over 3, 5 and 7 years?
With the same amount financed and the same fixed rate, the term spreads the debt over more or fewer payments. On $16,000 at 12 % nominal annual: over 36 months the payment is $531.43 and interest $3,131.44; over 60 months, $355.91 and $5,354.67; over 84 months, $282.44 and $7,725.27. The payment falls, the total interest rises.
Does a longer term mean paying more interest?
Yes, as long as the amount financed and the rate stay the same: the money takes longer to pay back, so it accrues interest for more months. The one exception is a 0 % rate, where total interest is zero on every term and only the size of the payment changes.
What is the difference between a nominal and an effective rate?
A nominal annual rate is split into twelve equal parts: 12 % per year is 1 % per month. An effective annual rate takes that same monthly rate and compounds it over twelve months, so it reflects interest building on itself: 1 % per month is 12.68 % effective annual. When comparing you can state which of the two you were given.
How do you work out the interest rate if you already know the payment?
Use the «Find the rate» mode with the price, the down payment, the term in months and the monthly payment. The tool searches for the monthly rate that makes the present value of every payment equal the amount financed, and from it shows the nominal and effective annual rates.
Can I use a custom number of months?
Yes. Beyond 36, 48, 60, 72 and 84 months you can type any whole number of months greater than zero and it joins the table marked as custom. If it matches one of the standard terms, that row is highlighted instead of duplicated.
Does the calculator include insurance, taxes and fees?
Only if you add them. In «Compare car payments», the «Taxes, fees and trade-in» section takes a sales tax rate, title and registration fees, a trade-in and a rebate, and you choose whether taxes and fees are financed. Insurance, origination fees and balloon payments are never included, and «Find the rate» works only from the four numbers in the offer. If your offer includes other charges, the real cost will be higher than the estimate.
Sources
The figures in the tables and the worked example are results calculated by this tool under the assumptions stated above, not data taken from anyone else. For the definitions behind the concepts, these public sources are a good starting point:
- Consumer Financial Protection Bureau — what a lender must disclose : defines amount financed, finance charge, total of payments and APR, the four numbers any offer should state.
- Consumer Financial Protection Bureau — auto loan guide : material from the US consumer financial protection agency on comparing vehicle financing offers.