Growing Annuity Calculator

Q: What is the growing annuity formula?

Present Value: PV = [PMT / (r − g)] × [1 − ((1+g)/(1+r))^n], where PMT is the first payment, r is the discount/interest rate, g is the growth rate per period, and n is the number of periods. Future Value: FV = PMT × [(1+r)^n − (1+g)^n] / (r − g). These formulas assume r ≠ g. When r = g, PV = PMT × n / (1+r).

Q: When does a growing annuity model apply?

Growing annuities model: salary-linked pension contributions that increase with annual raises; inflation-adjusted pension income (payments rise with CPI); lease payments with annual escalation clauses; dividend streams from companies with consistent dividend growth (Gordon Growth Model); growing SIP contributions where you increase the investment amount each year.

Q: How does growth rate affect the present value?

A higher growth rate increases the present value of a growing annuity because future payments are larger. However, the effect depends on the relationship between growth rate g and discount rate r. As g approaches r, the PV becomes very large (payments that grow at the discount rate are essentially worth more in PV terms). When g > r, the standard formula gives a negative denominator - this models an annuity that grows faster than the discount rate, which has implications for perpetuity valuations.

Calculate annuity value when payments grow at a constant rate each period.

🌱 What is a Growing Annuity?

A growing annuity is a series of periodic cash flows that increase at a constant rate each period. Unlike a standard (fixed) annuity where every payment is the same, in a growing annuity the first payment is PMT, the second is PMT × (1+g), the third is PMT × (1+g)², and so on, where g is the constant growth rate. This structure better reflects real-world cash flows that tend to grow over time due to inflation, salary increases, or contractual escalation.

Growing annuities appear in many financial contexts: salary-linked pension contributions that rise with annual pay increases; inflation-adjusted retirement income streams where payouts keep pace with the cost of living; dividend discount models in stock valuation (the Gordon Growth Model is essentially the PV of a growing perpetuity); and lease agreements with annual rent escalation clauses. Understanding the present and future value of growing annuities is essential for accurate financial planning.

The key variables in a growing annuity are the first payment (PMT), the interest or discount rate (r), the payment growth rate (g), and the number of periods (n). The formulas are mathematically elegant but require that r ≠ g. When r equals g, a simpler formula applies. When g exceeds r, the growing annuity is worth more and more over time - this edge case has special implications in perpetuity valuation and the dividend discount model.

📐 Growing Annuity Formula

PV = [PMT / (r − g)] × [1 − ((1+g)/(1+r))ⁿ]

FV = PMT × [(1+r)ⁿ − (1+g)ⁿ] / (r − g)

When r = g: PV = PMT × n / (1+r)

PMT = First period payment

r = Interest / discount rate per period

g = Payment growth rate per period

n = Number of periods

The growing annuity PV formula discounts each growing payment back to today. As g approaches r, the PV grows very large. For FV, the formula computes the accumulated value of all growing payments. Note: if g > r, the FV formula still works but produces a result that reflects faster-growing payments than the discount rate - this is valid and results in a larger FV than a fixed annuity would produce.

📖 How to Use This Calculator

Steps

Select Present Value or Future Value - choose based on whether you want today's equivalent lump sum (PV) or the terminal accumulated amount (FV).

Enter the first payment - the amount of the payment in period 1, before any growth is applied.

Enter interest rate and growth rate - the annual discount/investment rate and the rate at which payments grow each period. Growth rate of 0% gives a standard fixed annuity.

Click Calculate to see the PV or FV, total nominal payments, and the last (largest) payment amount.

💡 Example Calculations

Example 1 - Present Value of Salary-Linked Pension

First Payment = $5,000/yr | Rate = 8% | Growth = 3% | 20 years

PV = [$5,000 / (0.08 − 0.03)] × [1 − (1.03/1.08)²⁰]

= $100,000 × [1 − (0.9537)²⁰] = $100,000 × [1 − 0.3769] = $62,310

Last payment = $5,000 × (1.03)¹⁹ = $8,754

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Example 2 - Future Value of Growing Monthly Contributions

First Payment = $500 | Rate = 7% | Growth = 5% | 15 years

FV = $500 × [(1.07)¹⁵ − (1.05)¹⁵] / (0.07 − 0.05)

= $500 × [2.759 − 2.079] / 0.02 = $500 × 34.0 = $17,000

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❓ Frequently Asked Questions

What is a growing annuity?+

A growing annuity is a series of periodic payments that increase at a constant rate each period. The first payment is PMT, the second is PMT × (1+g), and so on. Growing annuities model salary-linked pension contributions, inflation-adjusted retirement income, and lease payments with escalation clauses.

What is the growing annuity formula?+

PV = [PMT / (r − g)] × [1 − ((1+g)/(1+r))^n]. FV = PMT × [(1+r)^n − (1+g)^n] / (r − g). When r = g, use PV = PMT × n / (1+r). PMT is the first payment, r is the interest rate, g is the growth rate, and n is the number of periods.

When does a growing annuity model apply?+

Growing annuities model: salary-indexed pension contributions that increase with annual raises; inflation-adjusted pension income; lease payments with annual escalation clauses; dividend streams from companies with consistent dividend growth (Gordon Growth Model); and growing SIP contributions where you increase the investment amount each year.

How does growth rate affect the present value?+

A higher growth rate increases the PV of a growing annuity because future payments are larger. However, as g approaches r, the PV grows very large (approaching infinity for a perpetuity when g = r). When g > r, the standard formula gives a negative denominator - this produces a valid result but represents an annuity that grows faster than the discount rate.