To calculate a perpetuity, divide the periodic payment by the discount rate. That single division gives you the present value of a stream of equal payments that continues forever. If the payments grow at a steady rate each year, you divide the next payment by the discount rate minus the growth rate instead. Everything else in perpetuity math is a variation on those two formulas.
What You Need Before You Start
Every perpetuity calculation needs two numbers at minimum: the periodic payment and the discount rate. The payment is the dollar figure distributed each period, such as a $10,000 annual scholarship or a $500 quarterly dividend. The discount rate reflects the return you could earn on a comparable investment of similar risk. If the payments grow, you also need the growth rate.
Both rates are expressed as decimals. A 6% discount rate becomes 0.06; a 2% growth rate becomes 0.02. The payment period and the rate period have to match. Quarterly payments call for a quarterly discount rate, not an annual one. Getting that alignment wrong is the most common source of nonsense answers in perpetuity math.
Fixed Perpetuity Formula
A fixed perpetuity pays the same amount forever. The present value is:
PV = Payment ÷ Discount Rate
Say a charitable endowment promises $10,000 a year and the appropriate discount rate is 5% (0.05). Divide 10,000 by 0.05 and you get $200,000. That is how much must be invested today to sustain the $10,000 payments indefinitely if the investment consistently earns 5%.
The logic is intuitive. $200,000 earning 5% generates exactly $10,000 in interest each year. Pay out the interest, leave the principal alone, and the payments continue forever. The same math prices a perpetual bond: if the formula returns a value above the bond’s market price, the bond looks undervalued; below, and you would be overpaying for its income stream.
Notice how sensitive the result is to the rate. Drop the discount rate from 5% to 4% and the present value jumps from $200,000 to $250,000. Push it to 8% and the value falls to $125,000. Small movements in the rate produce large swings in value, which is why picking it carefully matters more than anything else in the calculation.
Growing Perpetuity Formula
When payments increase at a steady rate each year, the formula is:
PV = Next Payment ÷ (Discount Rate − Growth Rate)
This is sometimes called the Gordon Growth Model, originally developed for valuing stocks with growing dividends. Suppose the first payment is $12,000, the discount rate is 8% (0.08), and the growth rate is 3% (0.03). Subtract 0.03 from 0.08 to get 0.05, then divide 12,000 by 0.05. The present value is $240,000.
One rule is non-negotiable: the growth rate must be lower than the discount rate. If they are equal, the denominator is zero and the formula breaks. If the growth rate exceeds the discount rate, the formula returns a negative number, which has no financial meaning. A perpetuity whose payments grow faster than the discount rate would have infinite value, and nothing in the real world behaves that way.
How High Can the Growth Rate Go?
Even when the growth rate stays below the discount rate, you cannot pick an aggressive number and call it sustainable forever. A perpetuity, by definition, runs indefinitely, and no single company or fund can outgrow the broader economy forever without eventually becoming the entire economy. The standard constraint among financial analysts is that the long-term growth rate in a perpetuity model should not exceed nominal GDP growth by more than a percentage point or two. With U.S. nominal GDP historically averaging roughly 3% real growth plus inflation, a perpetual growth rate above about 5–6% nominal is difficult to justify for any asset.
Plugging in an inflated growth rate makes the denominator tiny and the present value enormous. If your calculation produces a number that seems too good to be true, the growth rate assumption is almost always why.
Perpetuity Due: Payments at the Start of Each Period
The standard formulas assume each payment arrives at the end of the period. If payments come at the beginning, you are dealing with a perpetuity due, and the present value is slightly higher because each payment lands one period sooner. Calculate the ordinary perpetuity value, then multiply by (1 + discount rate):
PV of Perpetuity Due = (Payment ÷ Discount Rate) × (1 + Discount Rate)
Using the earlier $10,000-per-year example at 5%, the ordinary perpetuity value is $200,000 and the perpetuity due value is $200,000 × 1.05, or $210,000. The $10,000 difference reflects the fact that the first payment is immediate rather than a year away. For large payment amounts, that distinction matters. Ignoring it in a trust valuation could mean underfunding the arrangement from the outset.
Deferred Perpetuities
Sometimes the perpetual payments do not start right away. A trust might begin distributing funds five years from now, or a scholarship fund might not make its first award until the endowment reaches a target balance. Valuing a deferred perpetuity takes two steps.
First, calculate the present value of the perpetuity as of the date the payments begin, using the standard formula. Second, discount that lump sum back to today using the same rate. If the perpetuity starts in five years and its value at that point would be $200,000, find today’s value by dividing $200,000 by (1 + discount rate) raised to the fifth power. At 5%, that is $200,000 ÷ 1.2763, or roughly $156,710. The deferral period reduces how much you need to invest today because the money has time to grow before the first payment goes out.
Choosing the Right Discount Rate
The discount rate is the single most consequential input in any perpetuity calculation, and also the most subjective. The right rate depends on context.
- For a low-risk perpetuity like a government obligation, the discount rate typically starts with the yield on long-term government bonds. Long-duration benchmarks fit because the cash flows run forever.
- For stocks or business valuations, analysts commonly use the Capital Asset Pricing Model, which adds a risk premium to the risk-free rate based on how volatile the investment is relative to the broader market.
- For private trusts and endowments, the rate often reflects the expected return on the portfolio that will fund the perpetuity, adjusted for fees and taxes.
IRS Section 7520 Rates for Tax Valuations
If you are valuing a perpetuity for federal gift tax, estate tax, or income tax purposes involving charitable contributions, the IRS does not let you choose your own discount rate. Section 7520 of the Internal Revenue Code requires a rate equal to 120% of the federal midterm rate, rounded to the nearest two-tenths of a percent, for the month the valuation occurs.1Office of the Law Revision Counsel. 26 USC 7520 – Valuation Tables For charitable contributions, you can elect to use the rate from either of the two months before the valuation date if it produces a better result.
The IRS publishes updated Section 7520 rates monthly. For early 2026, the rates have been 4.6% for January and February, and 4.8% for March.2Internal Revenue Service. Section 7520 Interest Rates These rates change with market conditions, so check the current month before running a tax valuation. Using the wrong month’s rate on a gift tax return is the kind of error that triggers IRS adjustments.
Section 7520 rates also govern the valuation of charitable remainder trusts and charitable lead trusts. A charitable remainder trust must have a remainder interest worth at least 10% of the initial fair market value of the trust property, and that 10% test is calculated using the Section 7520 rate in effect when the trust is created.3Internal Revenue Service. Revenue Procedure 2016-42 When the Section 7520 rate is low, it is harder for a charitable remainder trust to pass the test, because the present value of the remainder going to charity shrinks.
Property transferred as a gift is valued at fair market value on the date of the gift.4Office of the Law Revision Counsel. 26 USC 2512 – Valuation of Gifts For perpetual interests in trusts or charitable arrangements, that value is typically computed using these perpetuity formulas together with the IRS actuarial tables prescribed under Section 7520.
Inflation and Fixed Perpetuities
A fixed perpetuity’s payments stay the same in nominal terms, but inflation steadily eats their purchasing power. A $10,000 annual payment buys much less in year 30 than today. At 3% annual inflation, that $10,000 has the real purchasing power of about $4,120 after 30 years.
If you are setting up an endowment or trust and want the distributions to hold their real value, a fixed perpetuity is the wrong tool. Use a growing perpetuity with a growth rate at least equal to expected inflation. Alternatively, calculate the real present value of a fixed perpetuity by using a real discount rate (roughly the nominal rate minus the inflation rate). That produces a higher present value, reflecting the true cost of funding constant-dollar payments forever.
A Legal Boundary Worth Knowing
The formulas assume payments last forever, but the law does not always let you structure things that way. The Rule Against Perpetuities generally prevents non-charitable interests from remaining contingent indefinitely. Under the traditional rule, a future interest must vest within a life in being plus 21 years. Many states have replaced this with a simpler 90-year limit, and a handful have abolished the rule entirely to attract trust business.
Charitable trusts are the major exception. A trust created for a charitable purpose can legally last forever, which is why university endowments and charitable foundations can genuinely operate as perpetuities. If you are structuring a private family trust meant to last indefinitely, check your state’s version of the rule before relying on these calculations. A trust that violates the Rule Against Perpetuities can be reformed by a court or, in some jurisdictions, voided entirely.