Free Growing Annuity Calculator

Understanding the Growing Annuity

A growing annuity is a series of periodic cash flows—deposits or withdrawals—that increase at a fixed percentage rate from one period to the next. This differs from a fixed annuity, where every payment remains constant over the term. Depending on when the cash flows occur, the annuity is classified as an ordinary growing annuity (payments at the end of each period) or a growing annuity due (payments at the beginning of each period).

Formulas for Present Value and Future Value

The valuation of a growing annuity depends on the relationship between the interest rate $r$ and the growth rate $g$. The tool can compute the Present Value of a Growing Annuity or the Future Value of a Growing Annuity using the formulas below, as well as the periodic payment (annuity amount).

Ordinary Growing Annuity (Payments at End)

Present Value (when $r \neq g$):

$$PV = P \times \frac{1 - \left(\frac{1+g}{1+r}\right)^n}{r - g}$$

Future Value (when $r \neq g$):

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

Where:

• $P$ = first payment or receipt,
• $r$ = periodic interest rate (rate of return),
• $g$ = periodic growth rate,
• $n$ = total number of periods.

When $r = g$: The standard formulas are undefined. Instead, the following simplified expressions are used:

$$PV = \frac{n \cdot P}{1 + r}, \qquad FV = n \cdot P \cdot (1+r)^{\,n-1}$$

Growing Annuity Due (Payments at Beginning)

For an annuity due, each cash flow occurs at the start of the period. Multiply any ordinary annuity result by $(1+r)$:

$$PV_{\text{due}} = PV_{\text{ordinary}} \times (1+r), \quad FV_{\text{due}} = FV_{\text{ordinary}} \times (1+r)$$

How to Use the Calculator

This online tool functions as a Growing Annuity PV Calculator, Growing Annuity FV Calculator, or Growing Annuity Payment Calculator depending on the variable you choose. It saves time by performing the appropriate calculation immediately after you enter your inputs.

Step-by-Step Process

1. Select the variable to solve for – Choose “Initial Deposit” (present value, PV), “Final Balance” (future value, FV), or “Annuity Amount” (periodic payment). The tool adjusts its calculation logic to match your goal.
2. Define cash flow direction – Specify whether the amounts are payments (deposits) or receipts (withdrawals).
3. Set annuity parameters – Pick the payment frequency (e.g., monthly, quarterly, annually), the annuity type (ordinary or due), the compounding frequency, and the start date.
4. Enter known values – Type in the known quantities: initial deposit, annuity amount, length of annuity, rate of return, and the annual growth rate. The periodic growth rate is automatically derived from the annual rate and the payment frequency you selected.
5. View the results – The computed value appears instantly in a summary table. A dynamic chart and a full payment schedule show how the balance evolves over the annuity term.

All calculations strictly follow the formulas shown above. The tool correctly applies the special-case formulas when the growth rate equals the interest rate.

Important Note

The calculator produces estimates based solely on the assumptions you provide. It is intended for educational and illustrative purposes and does not constitute professional financial advice. Actual investment results depend on market conditions and other factors not captured by this model. Always consult a qualified advisor for real-world decisions.