Interest Rate Calculator

How this result is built

Solve the annual interest rate that links a present value, payment, future value, and number of periods.

Sometimes you know the payment and the balance and you need the rate. That is a root-finding problem, not a rearrangement you want to do by hand. The solver searches for the nominal annual rate that balances the time-value equation.

What the opening example is for

Signs still matter. A loan you receive is a positive present value and a negative payment. Flip them and the rate will not describe the deal you think you entered.

The walkthrough below uses the numbers already sitting in Interest Rate 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 “N, periods” line on Interest Rate Calculator starts at 60. 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.

Interest Rate Calculator treats “Present value” as its own entry, and the form opens with $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.

Before you replace it, “Payment” reads -$400.00 on Interest Rate Calculator. 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.

Look at “Future value” first if you are checking Interest Rate Calculator: the filled value is $0.00. 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.

The remaining fields

The “P/Y, periods per year” line on Interest Rate Calculator starts at 1. 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.

Interest Rate Calculator treats “C/Y, compounds per year” as its own entry, and the form opens with 1. 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.

Before you replace it, “Payment timing” reads End of each period on Interest Rate Calculator. 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 opening result, line by line

Press Calculate on the opening form and Interest per year is 0.62%. That is the number the rest of this section is talking about.

N is 60.00 when you run the opening figures on Interest Rate 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 0.62%. 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.

Interest Rate 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 -$400.00 when you run the opening figures on Interest Rate 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

Interest Rate Calculator reports that sum of all periodic payments is -$24,000.00. 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.

Total interest is $4,000.00 when you run the opening figures on Interest Rate 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 0.62%. 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.

This is the nominal annual rate. The effective annual rate is shown beside it.

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 “N, periods”, from 60 to 66.00. Interest per year moves from 0.62% to 0.87%. Nothing else on the form was edited, so the gap between those two results is the effect of that one field on Interest Rate 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

Interest Rate Calculator compounds the rate you type. Markets do not pay a flat rate, and a fund fee comes out of the return before you should type it. The page is the equation, not a forecast and not a recommendation to buy or sell.

Interest Rate Calculator stops at its own formula. When the next question is different, open Finance Calculator (FV, PMT, I/Y, N, and PV, with the sign convention shown.); CAGR Calculator (One smooth rate between two values.); ROI Calculator (Total ROI and the annualized rate.). 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 Interest Rate Calculator by reading the labels, not the headline. The opening labels are N, periods (60), Present value ($20,000.00), Payment (-$400.00), Future value ($0.00), P/Y, periods per year (1), C/Y, compounds per year (1), Payment timing (End of each period). If a label is not the fact you have, the result cannot turn into that fact later. The illustration on the form lands on 0.62%. 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. Interest Rate Calculator is built for one job: The rate that makes the other four numbers true. The description on the page says the same thing in a sentence: Solve the annual interest rate that links a present value, payment, future value, and number of periods.

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, Interest Rate 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 0.62% as the output of the fields above and nothing else.

FAQs