Growing Annuity Calculator - Present and Future Value
Calculate the present value, future value, cumulative payments, and final payment for a cash flow that grows at a constant rate.
Enter the first end-of-period payment, growth rate, term, discount rate, and payment frequency to value a growing annuity.
Growing Annuity Calculator - Present and Future Value
Calculate the present value, future value, cumulative payments, and final payment for a cash flow that grows at a constant rate.
About Growing Annuities
A growing annuity is a finite series of payments that change by a constant percentage each period. The first payment occurs at the end of the first period, the next equals the first payment multiplied by one plus the growth rate, and the stream stops after a fixed number of payments. Salary-linked retirement contributions, leases with annual escalators, growing dividends, maintenance contracts, and education costs are common examples.
The present-value formula is P divided by r minus g, multiplied by one minus the ratio of one plus g to one plus r raised to n. P is the first payment, r is the discount rate per payment interval, g is the growth rate per interval, and n is the number of payments. When r equals g, the apparent division by zero is handled by its mathematical limit: P times n divided by one plus r. The future value is the present value compounded forward n intervals at r.
Payment frequency must be consistent with the other inputs. The valuation model divides the stated annual growth and interest rates by the payments-per-period value and multiplies the number of periods by that frequency. For example, 10 years with 12 payments per year creates 120 monthly payments. This nominal-rate conversion is a modeling convention; if an investment quotes an effective annual rate, convert it to an equivalent periodic rate before relying on the output.
Total payments are the undiscounted sum of the growing cash flows. They differ from present value because future dollars are discounted, and they differ from future value because earlier payments compound. If growth is below the discount rate, distant payments contribute progressively less to present value. Growth above the discount rate is mathematically valid for a finite stream, but the estimate becomes sensitive to long-term assumptions.
Use the present-value and future-value results to compare payment plans, value contractual escalators, or model contributions that rise with income. Confirm whether payments occur at the beginning or end of each interval; the growing annuity formulas assume end-of-period payments. Taxes, fees, skipped payments, variable growth, and changing discount rates are omitted. For irregular cash flows, discount each dated payment separately rather than forcing them into a constant-growth model.
Growing Annuity Examples
Worked cases illustrate the relationship among growth, discounting, and payment totals.
| Cash-Flow Inputs | Calculated Value | Interpretation |
|---|---|---|
| $1,000 first payment; 3.5% growth; 20 annual periods; 6% discount | PV $15,182.98; FV $48,693.86 | The 20 nominal payments total $28,279.68 before time-value adjustment. |
| $500 first payment; 0% growth; 10 periods; 5% discount | Total payments $5,000.00 | With zero growth, the stream becomes an ordinary level annuity. |
| $100 monthly first payment; 2% annual growth; 10 years; 5% annual discount; frequency 12 | PV $10,341.41; FV $17,032.40 | Annual rates are converted to periodic nominal rates before valuing 120 growing monthly payments. |
How to Value a Growing Annuity
- Enter the first payment due at the end of the first payment interval.
- Enter annual growth and discount rates, the number of years or periods, and payments per period.
- Select Calculate to see present value, future value, undiscounted payments, and the final payment.
- Verify that the frequency and rate conventions match the contract or investment being analyzed.
Growing Annuity FAQ
What happens when growth equals the interest rate?
The standard formula has a removable zero denominator. Its limit is first payment multiplied by the number of payments and divided by one plus the periodic rate.
Is a growing annuity the same as a growing perpetuity?
No. An annuity has a finite number of payments. A perpetuity continues indefinitely and requires a discount rate greater than its growth rate.
Does the growing annuity calculator assume payments at the beginning or end?
It assumes the first payment arrives at the end of the first interval. Beginning-of-period payments would each earn or discount for one additional interval.
Why is total payments different from future value?
Total payments simply adds nominal cash flows. Future value also compounds each earlier payment to the end of the term.