Perpetuity Calculator

How this result is built

Value a payment that continues forever and grows at a steady rate.

A perpetuity never ends. Its present value is the next payment divided by the discount rate minus the growth rate. This is the Gordon growth idea used for a dividend that grows forever, and it only works when the discount rate is higher than the growth rate.

What the opening example is for

Forever is a strong assumption. The value is still useful as a ceiling for a very long payment stream, such as a preferred dividend or a stable scholarship fund.

The walkthrough below uses the numbers already sitting in Perpetuity 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 “Next payment” line on Perpetuity Calculator starts at $1,000.00. 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.

Perpetuity Calculator treats “Discount rate” as its own entry, and the form opens with 8%. 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, “Growth of the payment” reads 2% on Perpetuity 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 Present value is $16,666.67. That is the number the rest of this section is talking about.

Next payment is $1,000.00 when you run the opening figures on Perpetuity 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, rate is 8.00%. 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.

Perpetuity Calculator reports that growth is 2.00%. 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

This is a Gordon growth perpetuity: the payment continues forever and grows at a steady rate.

The formula line on the page is PV = Payment / (Rate − Growth). 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 “Next payment”, from $1,000.00 to $1,100.00. Present value moves from $16,666.67 to $18,333.33. Nothing else on the form was edited, so the gap between those two results is the effect of that one field on Perpetuity 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

Perpetuity 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.

Perpetuity Calculator stops at its own formula. When the next question is different, open Present Value Calculator (What a future sum is worth today.); Dividend Calculator (Yield, growth, and the choice to reinvest.); Annuity Calculator (Equal payments, compounded forward.). 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 Perpetuity Calculator by reading the labels, not the headline. The opening labels are Next payment ($1,000.00), Discount rate (8%), Growth of the payment (2%). If a label is not the fact you have, the result cannot turn into that fact later. The illustration on the form lands on $16,666.67. 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. Perpetuity Calculator is built for one job: A forever payment, discounted once. The description on the page says the same thing in a sentence: Value a payment that continues forever and grows at a steady rate.

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, Perpetuity 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 $16,666.67 as the output of the fields above and nothing else.

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