Payment Calculator

How this result is built

Solve a monthly payment from a balance, a rate, a term, and an optional future value.

The payment calculator solves one unknown: the monthly payment. Leave the future value at zero for a loan that is fully paid off. Set a future value when a lease or a balloon leaves money at the end.

What the opening example is for

Payments are monthly and due at the end of the month. For a different frequency or beginning-of-period timing, use the finance calculator and solve for PMT.

The walkthrough below uses the numbers already sitting in Payment Calculator. Press Calculate and the headline should match this page. Then put your own figures in. The math does not run until you press the button, and Clear hides the result.

What each field is doing

The “Present value” line on Payment Calculator starts at $20,000.00. Leave that figure only when it matches the statement, the quote, or the plan you are testing. Press Calculate after the edit so the chart and the schedule move with it.

Payment Calculator treats “Interest rate” as its own entry, and the form opens with 7%. A round example is useful for learning the page. It is a poor substitute for the number on your own paperwork, so replace it and run the form again.

The remaining fields

Before you replace it, “Years” reads 5 on Payment Calculator. The other fields stay put while you change this one. That is the clean way to see what this line is doing inside the result.

Look at “Future value left at the end” first if you are checking Payment Calculator: the filled value is $0.00. If the label is a rate, type the annual figure the contract uses. If it is money, type the amount that will actually move, not a rounded hope.

The opening result, line by line

Press Calculate on the opening form and Periodic payment is -$396.02. That is the number the rest of this section is talking about.

N is 60.00 when you run the opening figures on Payment Calculator. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

On this opening pass, i/Y is 7.00%. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

Payment Calculator reports that pV is $20,000.00. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

PMT is -$396.02 when you run the opening figures on Payment Calculator. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

On this opening pass, fV is $0.00. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

How those lines were produced

Payment Calculator reports that sum of all periodic payments is -$23,761.44. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

Total interest is $3,761.44 when you run the opening figures on Payment Calculator. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

On this opening pass, effective annual rate is 7.23%. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

A negative payment is money you pay each period.

The formula line on the page is PV(1+i)^N + PMT(1+i·type)·((1+i)^N−1)/i + FV = 0. It is there so you can see the relationship the buttons are using. A schedule, when the page draws one, is that same series written row by row.

A second pass changes only “Present value”, from $20,000.00 to $22,000.00. Periodic payment moves from -$396.02 to -$435.63. Nothing else on the form was edited, so the gap between those two results is the effect of that one field on Payment Calculator. If the gap is tiny, this page is not very sensitive to that entry. If the gap is large, get that entry from a document before you plan around the result.

What this page will not claim

Payment Calculator applies the balance, the rate, and the payment you type. A lender’s payoff letter can include a fee or a daily interest convention this form does not see. Use the letter when you are sending the final check.

Payment Calculator stops at its own formula. When the next question is different, open Loan Calculator (A fixed payment, a rate, and the interest it creates.); Finance Calculator (FV, PMT, I/Y, N, and PV, with the sign convention shown.); Auto Loan Calculator (Price, tax, trade-in, and the payment that follows.). Do not add those results to this one as if they were the same kind of dollar.

Check the result before you use it

Start on Payment Calculator by reading the labels, not the headline. The opening labels are Present value ($20,000.00), Interest rate (7%), Years (5), Future value left at the end ($0.00). If a label is not the fact you have, the result cannot turn into that fact later. The illustration on the form lands on -$396.02. When you press Calculate and see that same figure, the button and this explanation are using one formula.

Change one field at a time. Write down the headline, edit a single line, and press Calculate again. A large jump means that line carries the result. A line that does not move is a line the formula ignores, which is a reason to confirm you opened the right page. Payment Calculator is built for one job: The payment that links a balance to a future value. The description on the page says the same thing in a sentence: Solve a monthly payment from a balance, a rate, a term, and an optional future value.

When the paperwork disagrees

Then hold the headline next to a source outside the site. That source might be a loan estimate, an account statement, a pay stub, or the public limit named in the methodology. A few cents of difference on a long schedule is ordinary rounding. A different rate, a fee you never typed, or a tax the form does not ask for is not rounding. Correct the input. Do not average the page with the paperwork.

When the outside source still disagrees, Payment Calculator has reached the edge of what it will claim. It will not phone a lender, pull a county record, or apply a credit you left blank. Send the calculator name, every input, and the result you expected through the contact page if you think the formula itself is wrong. Until that is settled, read -$396.02 as the output of the fields above and nothing else.

FAQs