Present Value of Growing Annuity Calculator: Optimize Your Future Payments

How to use the tool

1. Enter first payment (C): The amount due in period 1. Example entries: 1,500 or 5,250.
2. Type the discount rate (r %): Your expected return per period as a percentage. Example entries: 6.0 or 9.5.
3. Add the growth rate (g %): The percentage increase in each payment. Example entries: 3.0 or 4.2.
4. Set number of periods (n): How many equal periods the cash-flows last. Example entries: 12 or 30.
5. Press “Calculate”: The tool returns present value instantly.

Formula behind the calculator

For a growing annuity paid at period-end:

$$PV_{GA}=rac{C}{r-g}\left[1-\left(rac{1+g}{1+r}\right)^{n}\right]$$

• C = first payment
• r = discount rate (decimal)
• g = growth rate (decimal)
• n = number of periods

Worked examples

Example 1

• C = $1,500
• r = 6 % (0.06)
• g = 3 % (0.03)
• n = 12

$$PV=rac{1\,500}{0.06-0.03}\left[1-\left(rac{1.03}{1.06}\right)^{12}\right]=\$14,556$$

Example 2

• C = $8,000
• r = 10 % (0.10)
• g = 4 % (0.04)
• n = 8

$$PV=rac{8\,000}{0.10-0.04}\left[1-\left(rac{1.04}{1.10}\right)^{8}\right]=\$48,267$$

Quick-Facts

• Average U.S. CPI inflation 1913-2023: 3.1 % (BLS, 2023).
• Corporate discount rates commonly range 6-12 % (Damodaran, 2024).
• Long-run S&P 500 return ≈ 10 % annually (Ibbotson, 2023).
• Retirees often target 2-4 % real payment growth (Society of Actuaries, 2022).

FAQ

What is the present value of a growing annuity?

A present value converts increasing future payments into today’s dollars using time-value-of-money math (Brealey & Myers, 2020).

Why must the discount rate exceed the growth rate?

If g ≥ r the denominator r − g becomes zero or negative, causing mathematical divergence (CFA Institute, 2023).

How do I choose an appropriate discount rate?

Use your required return: investors apply their weighted average cost of capital, typically 6-12 % (Damodaran, 2024).

What happens when growth is zero?

The formula simplifies to an ordinary annuity: $$PV=rac{C}{r}\left[1-(1+r)^{-n}\right]$$ (Ross et al., 2019).

Is inflation the same as the growth rate?

Yes, when payments rise to offset cost-of-living; CPI averaged 3.1 % historically (BLS, 2023).

How accurate is the calculator?

It uses an exact algebraic solution; rounding is the only error source, typically < 0.01 % (Texas Instruments, BA II Plus guide).

What if payments grow faster than the discount rate?

PV becomes infinite; finance standards advise revising r or limiting the horizon (FASB ASC 820, 2022).

How can retirees apply this tool?

Input the first-year income need, expected investment return, inflation growth, and retirement length to find the lump sum required (AARP Retirement Guide, 2023).