Inputs
Results
| Period | Payment | Discount factor | PV of payment | Cumulative PV |
|---|---|---|---|---|
| Run a calculation to see the schedule… | ||||
Formula used
Let P be the first payment at period 1, growth rate g, discount rate r, and number of periods n.
- Present Value (ordinary):
PV = (P / (r − g)) × [1 − ((1 + g) / (1 + r))^n] - If payments are due (beginning), multiply PV by
(1 + r). - Future Value at period n (ordinary):
FV = (P / (r − g)) × [ (1 + r)^n − (1 + g)^n ] - If
r = g(special case):
PV = P × n / (1 + r), andFV = P × n × (1 + r)^(n − 1). For due timing, multiply each by(1 + r).
These formulas assume discrete compounding and payments once per period.
How to use this calculator
- Enter the first payment amount, growth rate, discount rate, and number of periods.
- Choose payment timing: ordinary means end of period; due means beginning of period.
- Select Calculate to view PV, FV, the schedule table, and chart.
- Use Download CSV or Download PDF to export your results.
- Try Load Example to see a prefilled scenario.
Example data table
Illustrative scenario with P = 1,000; g = 3% per period; r = 8% per period; n = 5; ordinary payments.
| Period | Payment | Discount factor | PV of payment | Cumulative PV |
|---|---|---|---|---|
| 1 | 1,000.00 | 0.925926 | 925.93 | 925.93 |
| 2 | 1,030.00 | 0.857339 | 883.06 | 1,808.98 |
| 3 | 1,060.90 | 0.793832 | 842.18 | 2,651.16 |
| 4 | 1,092.73 | 0.735030 | 803.19 | 3,454.35 |
| 5 | 1,125.51 | 0.680583 | 766.00 | 4,220.35 |
FAQs
What is a growing annuity?
A series of payments that increase by a constant growth rate each period and are discounted at a possibly different rate.
Which rate should I enter for r and g?
Enter rates per period. If you have annual percentages but monthly payments, convert to a monthly rate before entering.
What happens if r equals g?
The standard formula divides by r − g, so the special case is handled explicitly: PV = P × n / (1 + r) and FV = P × n × (1 + r)^(n − 1).
Can I model payments at the beginning of each period?
Yes. Choose due timing to shift payments one period earlier. PV and FV are then multiplied by (1 + r).
Are results tax or inflation adjusted?
No. Rates are as entered. To incorporate taxes or inflation, adjust the discount and growth rates accordingly.
Why does PV increase when r decreases?
Lower discount rates reduce the penalty for future cash flows, increasing their present value.
How accurate is the PDF export?
The PDF export uses browser rendering and jsPDF. Figures and tables match the on‑screen results for most modern browsers.