A growing annuity is a series of payments made at regular intervals over a fixed period where each payment is larger than the last by a constant percentage. If the first annual payment is $5,000 and the growth rate is 4%, the second payment is $5,200, the third is $5,408, and each following payment continues to escalate at the same rate. The structure shows up in commercial leases, lottery jackpot payouts, pension income, and salary-linked retirement contributions, and it has its own present value and future value formulas because the standard annuity formulas assume every payment is the same size.
The Four Inputs You Need
Every calculation runs on the same four variables. Change any one and the answer moves.
- First payment (C). The base amount before any growth is applied. In a lease, this is Year 1 rent. In a retirement plan, it is the initial annual distribution.
- Growth rate (g). The fixed percentage increase applied to each successive payment. A 3% rate means every payment is 3% larger than the one before it.
- Discount rate (r). The rate used to translate future dollars into today’s dollars. It reflects what the money could earn elsewhere.
- Number of periods (n). How many payments the annuity makes. A 20-year annual annuity has 20 periods; a 30-year monthly annuity has 360.
The relationship between r and g does most of the work. When the discount rate is well above the growth rate, later payments lose value quickly and the whole stream is worth less today. When the two rates sit close together, later payments hold their value and the present value climbs.
Present Value Formula
The present value tells you what the entire stream is worth right now. This is the formula most people need when pricing a lease, valuing an income stream, or choosing between a lump sum and a series of escalating payments.
PV = (C / (r − g)) × [1 − ((1 + g) / (1 + r))n]
The formula requires r and g to be different numbers. If they happen to be equal, use PV = (C × n) / (1 + r) instead.
Worked Example
Suppose an investment pays $5,000 at the end of year one and grows at 4% per year for 10 years, and you want an 8% return. What is the most you should pay today?
C = $5,000, r = 0.08, g = 0.04, n = 10.
PV = ($5,000 / (0.08 − 0.04)) × [1 − ((1.04) / (1.08))10]
$5,000 / 0.04 = $125,000. Then 1.04 / 1.08 = 0.96296, and 0.9629610 ≈ 0.6856, so 1 − 0.6856 = 0.3144.
PV = $125,000 × 0.3144 ≈ $39,300.
That $39,300 is the fair price today for 10 years of escalating payments totaling roughly $60,030 in nominal dollars. The gap is the time value of money: a dollar received in year 10 is worth less than a dollar received today.
Future Value Formula
The future value tells you what the growing stream will be worth at the end of the final period, assuming each payment is reinvested at the discount rate. This is the version to use for retirement planning, where escalating contributions accumulate over decades.
FV = (C / (r − g)) × [(1 + r)n − (1 + g)n]
Using the same numbers: FV = ($5,000 / 0.04) × [(1.08)10 − (1.04)10] = $125,000 × [2.1589 − 1.4802] = $125,000 × 0.6787 ≈ $84,838. As a check, $39,300 × (1.08)10 ≈ $84,838, which confirms the present value and future value are consistent.
End of Period vs. Beginning of Period
Both formulas above assume payments arrive at the end of each period, which is called an ordinary annuity. Most contracts work this way: a month of work before the paycheck, a month of occupancy before rent is due.
An annuity due flips the timing so payments arrive at the beginning of each period. Every payment lands one full period earlier, has less time to be discounted, and the whole stream is worth more. The conversion is simple: multiply the ordinary annuity value by (1 + r). At an 8% discount rate, the $39,300 above becomes $39,300 × 1.08 ≈ $42,444 if payments shift to the start of each period. An 8% swing is why the timing clause in a lease is worth reading carefully.
Growing Perpetuity
If the payments continue forever, the formula collapses to something much simpler.
PV = C / (r − g)
This only holds when the discount rate exceeds the growth rate. If g is greater than or equal to r, the present value is theoretically infinite, which is the math’s way of telling you the assumptions don’t survive contact with the real world.
The growing perpetuity is the backbone of the Gordon Growth Model used to value stocks. An investor who expects a stock to pay $2.00 in dividends next year, with dividends growing 5% annually and a required return of 10%, would value the stock at $2.00 / (0.10 − 0.05) = $40 per share. The model works best for mature companies with stable dividend growth.
Running the Numbers in a Spreadsheet
Excel’s built-in PV and FV functions assume every payment is identical, so they won’t handle a growing stream directly.1Microsoft Support. FV Function Two approaches work.
The quick one is to type the formula into a single cell. For the earlier example: =(5000/(0.08-0.04))*(1-((1.04/1.08)^10)). One cell, no custom functions.
The more flexible approach is to build a table. Column A holds the period number (1 through n), column B calculates that period’s payment as C × (1 + g)(period − 1), and column C discounts each payment back to today as payment / (1 + r)period. Sum column C for the present value. This lets you see the math period by period and adjust the growth rate partway through if needed.
Keep the units consistent either way. Monthly payments need monthly growth and discount rates, and the period count needs to be in months.
Where Growing Annuities Show Up
The formula sounds academic until you notice how many real arrangements it describes.
Lottery Jackpots
When a Mega Millions or Powerball winner picks the annuity option, they receive one immediate payment followed by 29 annual payments, each 5% larger than the last.2Mega Millions. Difference Between Cash Value and Annuity That is a textbook growing annuity due. The 5% escalation is designed to protect purchasing power across a 30-year payout. Deciding between the lump sum and the annuity comes down to running the present value calculation above.
Social Security Benefits
Social Security applies a cost-of-living adjustment each year based on inflation. For 2026, that adjustment is 2.8%.3Social Security Administration. Social Security Announces 2.8 Percent Benefit Increase for 2026 The COLA percentage changes annually rather than staying fixed, but the structure closely resembles a growing annuity, and planners commonly model it that way using a long-run average growth rate.
Commercial Lease Escalations
Multi-year commercial leases routinely include rent escalation clauses that raise rent by a negotiated percentage each year. The specific rate is a matter of contract negotiation, since no broad federal or state rules cap commercial rent increases. Landlords use the present value formula to test whether a proposed escalation schedule produces enough income to justify locking in a long-term tenant.
Stock Valuation
The Gordon Growth Model applies the growing perpetuity formula to a company’s future dividends. Analysts pull dividend histories and growth projections from Securities and Exchange Commission filings and use PV = C / (r − g) to estimate what a stock is worth today.4U.S. Securities and Exchange Commission. Data Library
Salary-Linked Retirement Contributions
If your salary rises by a consistent percentage each year and you contribute a fixed share to a retirement plan, your contributions form a growing annuity. The future value formula gives a more realistic accumulation projection than assuming flat contributions for 30 years.
What Can Go Wrong
The model is powerful, but it rests on assumptions that don’t always survive the real world.
The biggest risk is inflation outrunning the growth rate. A 2% annual escalation sounds fine until inflation runs at 5% for several years. Each payment gets nominally larger but buys less. The defense is negotiating a growth rate that exceeds your long-run inflation expectations, or tying the escalation to an inflation index rather than a fixed percentage.
The math has its own constraint. For the standard present value formula to give a finite answer, r must exceed g; when they are equal, use PV = (C × n) / (1 + r); when g is greater than or equal to r in a perpetuity, the formula breaks because the payments grow too fast relative to the discount rate for the sum to converge. Aggressive escalation combined with a long duration is difficult to price reliably.
Every growing annuity also carries counterparty risk. The formula tells you what the payments are worth if they arrive; the payments only arrive if the entity on the other side stays solvent for the full term. A 30-year escalating lease is only as good as the tenant’s ability to pay in year 30, and a pension’s growing distributions depend on the plan remaining funded and on the plan documents promising escalation in the first place.
A Note on Taxes
The growth built into the payments doesn’t get any special tax break. Annuity distributions are generally taxed as ordinary income rather than at the lower capital gains rates.5Internal Revenue Service. Publication 575 (2025), Pension and Annuity Income If you paid in with after-tax dollars, the IRS uses an exclusion ratio to split each payment into a tax-free return of your investment and a taxable earnings portion.6Internal Revenue Service. Publication 939, General Rule for Pensions and Annuities Withdrawals from a qualified annuity in a retirement account before age 59½ generally face a 10% early withdrawal penalty on top of ordinary income tax, unless an exception applies.7Internal Revenue Service. Retirement Topics – Exceptions to Tax on Early Distributions