Find the present value and future value of a series of payments that grow at a constant rate, such as rising salary savings, inflation-linked income or escalating rent. Switch between ordinary annuities and annuities due, or solve for the first payment you need.
Last updated:
Solve for
Annuity details
$
Later payments grow by the growth rate.
$
%
%
e.g. expected raises or inflation. May be 0 or negative.
years
Enter your values to see the result.
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How to use the Growing Annuity Calculator
Choose what to solve for: PV and FV from a payment, or the first payment needed for a target value.
Enter the first payment (or the target value), the annual discount or interest rate and the annual growth rate of the payments.
Set the term and payment frequency. Rates are divided by the number of payments per year.
Pick the timing: end of period for an ordinary annuity, start of period for an annuity due.
Review the results, the formula working and the year-by-year schedule, and download it as CSV if needed.
Growing annuity formulas
With first payment C, discount rate r and growth rate g per period, and n payments:
Present value (ordinary): PV = C ÷ (r − g) × [1 − ((1 + g) ÷ (1 + r))n]
When r = g: PV = n × C ÷ (1 + r) and FV = n × C × (1 + r)n − 1
First payment for a target: C = PV ÷ PV factor, or C = FV ÷ FV factor
Worked example: payments start at 10,000 and rise 3% a year for 20 years, discounted at 6%. PV = 10,000 ÷ 0.03 × [1 − (1.03 ÷ 1.06)20] = 145,615.33.
The same stream invested at 6% grows to 467,008.08. You pay in 268,703.74 in total and the last payment is 17,535.06.
Without growth, 20 level payments of 10,000 are worth only 114,699.21 today. Paid at the start of each year (annuity due), the PV is 154,352.25.
PV factor per 1 of first payment (20 annual payments)
Discount rate
g = 0%
g = 2%
g = 3%
g = 4%
4%
13.59
16.09
17.57
19.23
6%
11.47
13.42
14.56
15.84
8%
9.82
11.35
12.25
13.25
Multiply the factor by your first payment for a quick present value. At r = g = 4% the factor is simply 20 ÷ 1.04 = 19.23.
Tips
Use real rates for "today's money". If payments grow with inflation, discounting at a real rate (nominal minus inflation, roughly) with g = 0 gives a similar answer to a nominal rate with g = inflation.
Frequency matters. With monthly payments the calculator applies the annual growth rate ÷ 12 every month. If your payments rise once a year (like annual raises), use annual payments for the closest match.
Check the schedule. The year-by-year table shows how much interest builds up and makes it easy to compare with a statement or spreadsheet.
Frequently asked questions
What is the formula for the present value of a growing annuity?
PV = C ÷ (r − g) × [1 − ((1 + g) ÷ (1 + r))^n], where C is the first payment (one period from now), r the discount rate per period, g the growth rate per period and n the number of payments. For C = 10,000, r = 6%, g = 3% and n = 20 years, PV = 145,615.33.
How do you calculate the future value of a growing annuity?
FV = C × [(1 + r)^n − (1 + g)^n] ÷ (r − g), which is the same as PV × (1 + r)^n. In the example above, 10,000 a year growing 3% for 20 years and earning 6% grows to about 467,008.08.
What happens when the growth rate equals the discount rate?
The usual formula divides by zero, but the answer is simple: every discounted payment is worth the same, C ÷ (1 + r), so PV = n × C ÷ (1 + r) and FV = n × C × (1 + r)^(n − 1). The calculator switches to this formula automatically.
What is the difference between a growing annuity and a growing annuity due?
In an ordinary growing annuity each payment arrives at the end of a period; in an annuity due it arrives at the start. Because every payment comes one period earlier, both the present value and the future value of an annuity due are the ordinary values multiplied by (1 + r).
Can the growth rate be negative?
Yes. A negative growth rate models payments that shrink each period, such as declining production from a well or a pension that is not fully indexed. The formula works the same way as long as the growth rate is above −100%.
How is a growing annuity different from a growing perpetuity?
A growing annuity stops after n payments, while a growing perpetuity continues forever. A growing perpetuity is the limit of a growing annuity as n becomes very large, so its value is C ÷ (r − g), and it only exists when r is greater than g.
Where are growing annuities used?
Common uses include valuing retirement income that rises with inflation, planning savings that increase with your salary, pricing leases with annual rent escalations, and valuing a company's cash flows over a forecast period before a terminal value.
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