Use this calculator to find the first payment of a growing annuity: enter present value, interest rate, growth rate, and periods; it returns the starting payment that will rise each period. Average U.S. inflation has been 3.2 % per year since 1914 (BLS CPI, 2023), so matching your growth rate to that figure maintains purchasing power.
Growing Annuity Payment Calculator
Initial Payment:
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How to use the tool
Follow the numbered bullets and plug in two fresh sample values for each field to check different scenarios.
Present Value – current fund size, e.g., $80 000 or $200 000.
Rate Per Period (%) – expected return per period, such as 4 % or 6.5 %.
Growth Rate (%) – planned payment increase, for instance 1.8 % or 3.2 %.
Number of Periods – total payouts, say 8 or 25 periods.
Press Calculate; the tool shows your initial payment instantly.
Formula used
The first payment (P_1) is solved from the present value equation:
$$
P_1 = PV \, rac{r – g}{1 – \left(\frac{1+g}{1+r}\right)^{n}}
$$
where (PV) = present value, (r) = rate per period, (g) = growth rate, (n) = number of periods (Investopedia, 2023).
Your first payment would be roughly $11 995, increasing 3 % annually for 10 years.
Quick Facts
Average U.S. CPI inflation 1914-2023: 3.2 % per year (BLS CPI, 2023).
10-year U.S. Treasury yield averaged 4.3 % in 2023 (FRED, 2024).
Social Security 2023 COLA: 8.7 %—largest since 1981 (SSA News Release, 2022).
Corporate finance texts assume (r>g) for solvency (Brealey et al., 2020).
FAQ
What is a growing annuity?
A growing annuity pays cash flows that rise by a fixed percentage every period until the final payment, mirroring inflation or income growth (Investopedia, 2023).
Why must the interest rate exceed the growth rate?
When (gge r) the denominator in the formula approaches zero, making present value explode and rendering the series unsustainable (Brealey et al., 2020).
Can I switch from annual to monthly periods?
Yes; convert both rate and growth to monthly equivalents: divide annual figures by 12, and set periods to months (Financial Modeling Guide, URL).
How does inflation influence my growth rate choice?
Set (g) near expected inflation; U.S. long-run CPI averages 3.2 % so a 3 % growth keeps real value stable (BLS CPI, 2023).
What if I expect payments to shrink?
Enter a negative growth rate; the formula still works provided (r) stays positive and larger in absolute terms (Damodaran, 2023).
How accurate is this calculator?
It uses the exact present-value expression shown above; rounding to two decimals means errors stay below $0.01 for typical inputs.
Is compounding frequency built in?
Yes; input rates consistent with your period. If compounding occurs semi-annually, use the semi-annual rate and periods count.
Where is this formula used professionally?
Analysts apply it when valuing dividend-growing stocks and structuring step-up loans; “the present value of a growing annuity equals the discounted value of each expanding payment” (Brealey et al., 2020).
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