Growing Annuity Calculator — Future Value of a Growing Annuity
Calculate the future value and present value of a growing annuity — a series of payments that increase at a constant rate each period. Ideal for modeling salary-linked savings, escalating rents, or dividend growth investments.
What Is a Growing Annuity?
A growing annuity is a finite series of periodic cash flows where each payment increases at a constant percentage rate g from the previous payment. If the first payment is PMT, the second is PMT × (1+g), the third is PMT × (1+g)², and so on.
Growing annuities model numerous real-world financial scenarios:
- Salary-linked retirement savings — 401(k) contributions that increase with annual raises (typically 2–5%).
- Escalating lease payments — Commercial leases with built-in annual rent increases.
- Dividend growth stocks — Companies that increase dividends at a consistent rate each year.
- Revenue projections — Business revenue growing at a steady annual rate.
- Social Security adjustments — Benefits that grow with cost-of-living adjustments (COLA).
Growing Annuity Future Value Formula
The future value of a growing annuity depends on whether the interest rate r equals the growth rate g:
When r ≠ g (Standard Case)
When r = g (Special Case)
Where:
- PMT = First-period payment amount
- r = Interest rate per period
- g = Growth rate of payments per period
- n = Total number of periods
The formula works by summing the future value of each individual growing payment: the payment at time k is PMT × (1+g)k, compounded forward for (n−k−1) remaining periods at rate r. The closed-form solution avoids computing each term individually.
Growing Annuity Present Value Formula
The present value tells you what the entire stream of growing payments is worth today:
When r ≠ g
When r = g
The PV and FV are related by the standard time-value-of-money identity:
Growing Annuity vs. Level Annuity
The difference between a growing and level annuity can be dramatic over long time horizons. Here's a comparison with a first payment of $5,000, 8% interest rate, over 25 years:
| Growth Rate (g) | Total Payments | Future Value | Extra vs. Level |
|---|---|---|---|
| 0% (Level) | $125,000 | $365,530 | — |
| 2% | $160,121 | $427,219 | +$61,689 |
| 3% | $181,837 | $474,476 | +$108,946 |
| 5% | $238,635 | $591,967 | +$226,437 |
| 7% | $316,245 | $746,922 | +$381,392 |
Growing Perpetuity — The Infinite Case
When a growing annuity extends to infinity, it becomes a growing perpetuity. While the future value of a growing perpetuity is infinite (it never stops growing), its present value has a elegant closed-form solution:
This formula is the foundation of the Gordon Growth Model (GGM), widely used to value stocks based on expected future dividends:
Where D₁ is the expected next dividend, ke is the cost of equity, and g is the dividend growth rate. For example, if a company pays a $2.00 dividend growing at 4% with a 10% required return: Price = $2.00 / (0.10 − 0.04) = $33.33.
Applications: Salary Growth, Dividend Growth Model
Salary-Linked Retirement Savings
If you earn $60,000 and contribute 10% to your 401(k) with a 3% annual raise, your first contribution is $6,000/year. Over 30 years at 8%:
Versus a fixed $6,000/year: FV = $6,000 × 113.283 = $679,699. The 3% growth adds $234,587.
Dividend Growth Stock Valuation
A stock pays a $3.00 dividend this year, expected to grow at 5% annually. If your required return is 11%, the present value of 20 years of dividends:
Frequently Asked Questions
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A growing annuity is a finite series of periodic payments where each payment increases by a constant percentage (growth rate g) from the previous one. If the first payment is $1,000 with a 5% growth rate, the payments would be $1,000, $1,050, $1,102.50, and so on. It's used to model increasing salary contributions, escalating rents, and dividend growth scenarios.
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When the interest rate r differs from the growth rate g: FV = PMT × [((1+r)n − (1+g)n) / (r − g)]. When r equals g, the formula simplifies to: FV = PMT × n × (1+r)n−1. Here, PMT is the first payment, r is the rate per period, g is the growth rate per period, and n is the number of periods.
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When g = r, the standard formula produces a 0/0 indeterminate form. The special-case formula FV = PMT × n × (1+r)n−1 resolves this by using L'Hôpital's rule. In practical terms, when g = r, the growth in payments exactly offsets the compounding rate, leading to a linear relationship with n.
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A growing annuity has a finite number of payments (n periods), while a growing perpetuity continues forever. The growing perpetuity PV = PMT/(r−g) only works when r > g. The growing perpetuity has an infinite future value, but a finite present value, making it useful for stock valuation (Gordon Growth Model).
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Yes. Multiply the standard growing annuity formula by (1+r) to shift all payments to the beginning of each period: FVdue = FVgrowing × (1+r). This is the same adjustment used for ordinary vs. due annuities.
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Set your first year's retirement contribution as the payment, your expected investment return as the interest rate, your expected annual raise as the growth rate, and years until retirement as the period count. The result shows your projected retirement fund. A common approach: 10% of starting salary growing at 3% per year for 30–40 years.