Growing Annuity Calculator
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
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
💡 Example Calculations
Example 1 - Present Value of Salary-Linked Pension
First Payment = $5,000/yr | Rate = 8% | Growth = 3% | 20 years
Example 2 - Future Value of Growing Monthly Contributions
First Payment = $500 | Rate = 7% | Growth = 5% | 15 years
❓ Frequently Asked Questions
🔗 Related Calculators
What is a growing annuity?
A growing annuity is a series of periodic payments that increase at a constant rate each period. For example, if your first payment is $1,000 and payments grow at 3% per year, the second payment is $1,030, the third is $1,060.90, and so on. Growing annuities model real-world cash flows like salary-linked pension contributions, inflation-adjusted retirement income, and lease payments with escalation clauses.
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).
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.
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.
What is a growing annuity used for in real life?
Growing annuities model salary-linked savings, where contributions increase each year with a raise. If you earn Rs 60,000/month and save 10%, your savings grow as your salary grows. The growing annuity formula captures this escalation effect on your final corpus.
What is the difference between a growing annuity and a growing perpetuity?
A growing annuity has a fixed number of payments; a growing perpetuity continues forever. For a perpetuity, PV = PMT / (r - g). A growing annuity uses a finite-period formula. Growing annuities are used for finite savings horizons like 20-30 year careers.
When does the growing annuity formula break down?
The standard formula requires r not equal g. When r = g, PV = n x PMT / (1 + r). If the growth rate exceeds the discount rate, present value increases with time, which can be economically unrealistic for long horizons.
How does a 5% salary growth rate affect a 30-year savings corpus?
Substantially. Saving Rs 5,000/month starting at age 25 with 0% growth at 8% yields Rs 9.1 lakh by 55. With 5% annual payment growth, the final corpus rises to Rs 28+ lakh. The growth effect compounds twice - on both contribution size and investment returns.