Growing Annuity Calculator PV, FV, Solver & Comparator
Calculate the present value (PV) and future value (FV) of a series of payments growing at a fixed growth rate g each period — e.g. pension contributions rising with salary increases, or growing dividends. The calculator assumes payments at the end of each period.
These results are educational estimates, not investment or financial advice. Actual figures may differ due to taxes, inflation, fees, and risk.
Present Value Growing Annuity
Present value of Rp PMT1 payments, growing g% each period for n periods, discounted at r% per period.
Future Value Growing Annuity
Future value (at the end of period n) of the same growing payment series.
Solver: find the unknown variable
Enter the target PV and three known variables, then choose the fourth variable to solve for.
Comparator: growing vs level annuity
Compare the present value of a growing annuity with a level annuity (fixed payments of PMT₁) at the same r and n.
Frequently asked questions about growing annuity
What is a growing annuity?
A growing annuity is a series of periodic payments growing at a fixed growth rate g each period: Rp1,000, Rp1,050, Rp1,102.50, and so on (with PMT1 of Rp1,000 and g = 5%). Unlike a level annuity whose payments are fixed each period. Examples include pension contributions rising 3% per year with salary increases, or growing stock dividends. This calculator assumes payments at the end of each period.
What is the growing annuity present value formula?
PV = PMT1 × [1 − ((1+g)/(1+r))^n] / (r − g), where PMT1 = first payment, g = growth rate per period, r = discount rate per period, and n = number of periods. Example: PMT1 of Rp1,000, g = 5%, r = 10%, n = 10. Compute ((1.05)/(1.10))^10 = 0.6280; 1 − 0.6280 = 0.3720; divide by (0.10 − 0.05) = 0.05 giving a factor of 7.4398; PV = Rp1,000 × 7.4398 = Rp7,439.81.
What happens if discount rate r equals growth g?
The main formula cannot be used because its denominator (r − g) becomes zero. The correct value is its limit: PV = n × PMT1 / (1 + r). Example: PMT1 of Rp1,000, r = g = 10%, n = 10 → PV = 10 × Rp1,000 / 1.1 = Rp9,090.91. This case rarely occurs exactly in practice, but the calculator handles it automatically.
How does it differ from a level annuity?
A level annuity uses FIXED payments each period (PV formula = PMT × [1 − (1+r)^−n] / r), while a growing annuity’s payments RISE g% each period. With PMT1 of Rp1,000, r = 10%, n = 10: a level annuity is worth Rp6,144.57 today, while a growing annuity with g = 5% is worth Rp7,439.81 — a difference of Rp1,295.25 (21.08% higher). If your payments are fixed each period, use the level annuity calculator.
When is a growing annuity used in real life?
For cash flows that genuinely grow over time: salary projections and pension contributions rising with salary increases, growing-dividend stock valuations (the Gordon growth model is a growing perpetuity: PV = D1 / (r − g)), property rent with annual escalation, or business revenue projections. These are conceptual use examples, not endorsements of specific financial products.
What does it mean if g exceeds r?
It means payments grow faster than the discount rate, so far-future payments still contribute substantially to present value. The formula still holds as long as r ≠ g. Example: PMT1 of Rp1,000, g = 12%, r = 8%, n = 10 → PV = Rp10,965.22. Note: for an infinite series (perpetuity) with g ≥ r, present value becomes mathematically infinite, so the model is no longer meaningful as a valuation.
Can this calculator’s results guide investment decisions?
No. The results are educational estimates based on the numbers you enter, not investment or financial advice. Real financial decisions involve taxes, inflation, risk, fees, and other factors not modelled here. For important decisions, consider consulting a licensed financial planner.