Growing Annuity Calculator

What is a Growing Annuity?

A growing annuity is a finite series of periodic cash flows that increase at a constant growth rate over time. Unlike a standard fixed annuity where every cash payment remains constant, a growing annuity adjusts each payment to account for inflation, salary growth, dividend growth, or scheduled investment increases.

Growing annuities are common in financial planning, inflation-indexed retirement payouts, structured settlement agreements, and dividend investment strategies.

Growing Annuity Formulas

Calculating the present value (PV) and future value (FV) of a growing annuity depends on whether payments occur at the end of each period (ordinary annuity) or at the beginning of each period (annuity due).

1. Ordinary Growing Annuity (End of Period)

When discount rate $r \neq g$ (growth rate):

$$\text{PV} = \frac{P_1}{r - g} \left[ 1 - \left( \frac{1+g}{1+r} \right)^n \right]$$

$$\text{FV} = P_1 \times \frac{(1+r)^n - (1+g)^n}{r - g}$$

When discount rate equals growth rate ($r = g$):

$$\text{PV} = \frac{n \times P_1}{1 + r}$$

$$\text{FV} = n \times P_1 \times (1 + r)^{n-1}$$

2. Growing Annuity Due (Beginning of Period)

For payments deposited at the start of each period, multiply the ordinary annuity results by $(1 + r)$:

$$\text{PV}_{\text{due}} = \text{PV}_{\text{ordinary}} \times (1 + r)$$

$$\text{FV}_{\text{due}} = \text{FV}_{\text{ordinary}} \times (1 + r)$$

Where:

• $P_1$: The first cash flow payment amount.
• $r$: Periodic interest or discount rate.
• $g$: Periodic growth rate of the payment.
• $n$: Total number of periods or years.

Applications and Related Tools

Growing annuities help evaluate pension cash flows adjusted for cost of living, rental income escalating annually, and savings contributions increased every year as income rises.

Compare growing annuities with fixed cash flows using our Future Value of Annuity Calculator or evaluate lump-sum present values with the Present Value Annuity Calculator.