# Growing Annuity Calculator

Created by Tibor Pál, PhD candidate
Reviewed by Jack Bowater and Dominik Czernia, PhD
Based on research by
Cipra T. Financial and Insurance Formulas; 2006
Last updated: Jan 18, 2024

Use the growing annuity calculator (or PV of growing annuity calculator) to determine any of the following variables of a specified growing annuity:

• Initial deposit or the present value of the growing annuity (PV);
• Final balance or the future value of the growing annuity (FV); and
• Annuity amount which is the periodic cashflow (deposit or withdrawal).

In addition, you can analyze the result by following the progression of balances in the dynamic chart or the annuity table.

In the following, you can learn the future value of the growing annuity formula (increasing annuity formula), and we also show you some growing annuity examples. You can also read what a growing annuity is and find out the types of annuity.

If you would like to check another common type of annuity, check our variable annuity calculator.

## What is growing annuity?

A growing annuity refers to the series of payments (deposits) or receipts (withdrawals) made over a specified term that increase each period at a constant rate.

In a growing ordinary annuity, payments or receipts happen at the end of each period; in a growing annuity due, payments or receipts are made at the beginning of each period.

## What is the growing annuity formula? Future and present values of growing annuity

The ordinary present value of growing annuity formula can be found the following equation:

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

where:

• $PV_{ga}$ - Present value of the growing annuity;
• $P$ - The first payment or receipt subject to constant periodic increase;
• $r$ - Rate of return or interest rate;
• $g$ - Periodic growth rate of the cash flows; and
• $n$ - Number of periods.

And the future value of growing annuity formula:

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

where:

• $FV_{ga}$ - Future value of the growing annuity.

Note, that the above formula is inadequate when the rate of return and the growth rate are equal. In such a case, the following formula is applicable:

$FV_{ga} =P\times n\times (1 + r)^{n-1}$

You need to multiply the above equations by $(1 + r)$ to get the growing annuity due formula.

## How to use the growing annuity calculator?

You need to proceed with the following simple steps to run the tool:

1. Growing annuity configuration

• Subject of interest:
• Initial deposit - The present value of growing annuity;
• Final balance - The future value of growing annuity; and
• Annuity amount - Periodic deposit or withdrawal.
• Direction of cash flows:
• Payments (deposits); and
• Receipts (withdrawals).
• Annuity payment frequency - The regularity of annuity payouts;
• Type of annuity - You can choose between an annuity due (beginning of period) or an ordinary annuity (end of period);
• Compounding frequency - The frequency interest is added to the principal balance of your annuity, or, in other words, how often the earned return or interest is reinvested; and
• First period starts from (advanced mode) - The first day of the annuity.

2. Main specifications

• Initial deposit - The present value of the annuity, that is, the balance at the beginning of the annuity.
• Annuity amount - The amount of regular deposit or withdrawal.
• Length of annuity - The lifespan of the annuity.
• Rate of return - The interest rate of the growing annuity.
• Annual growth rate - You can set the annual percentage increase of the growing annuity here.
• Periodic growth rate - The percentage growth rate of the periodic deposits of withdrawals. Note, that periodic and annual growth rates are linked together: the other will be calculated according to annuity frequency if you set one.

3. Results

When you set all the required parameters, you will immediately see the results summarized in a table. You can also follow the progress of your annuity balance in a dynamic chart and annuity table of the payment schedule.

## FAQ

### How do I calculate the cash flows of a growing annuity?

Follow the instructions bellow to find the cash flows of the growing annuity:

1. For the first cash flow, you need to apply the following formula:

P = FV / [((1 + r)n - (1 + g)n) / (r - g)],

where:

• FV - Final balance;
• P - First payment or receipt;
• r - Interest rate;
• g - Growth rate; and
• n - Number of periods.
1. If the growth rate and the interest rate are equal, you need to apply the following modified simple formula:

P = FV / (n * (1 + r)ⁿ⁻¹).

1. If you wish to compute the cash flow in period t:

Pt = P * (1 + r)t-1.

### How do I calculate the future value of growing annuity?

To compute the future value of growing annuity you need to apply the formula:

FV = P * [((1 + r)n - (1 + g)n) / (r - g)],

where:

• FV - Future value of the growing annuity;
• P - First payment or receipt;
• r - Interest rate;
• g - Growth rate; and
• n - Number of periods.

### Are the periodic cash flows equal in growing annuity?

No. In a growing annuity scheme, the reoccurring payments or recipes increase at a constant rate each period.

## Growing annuity calculator disclaimer

You should consider the growing annuity calculator as a model for financial approximation. All payment figures, balances, and interest figures are estimates based on the data you provided in the specifications that are, despite our best effort, not exhaustive.

For this reason, we created the calculator for instructional purposes only. Still, if you experience a relevant drawback or encounter any inaccuracy, we are always pleased to receive useful feedback and advice.

Tibor Pál, PhD candidate
Growing annuity configuration
I'd like to know the...
final balance (FV)
Direction of cash flows
Payment (deposit)
Annuity payment frequency
Monthly
Type of annuity
Annuity due
Compounding frequency
Monthly
Main specifications
Initial deposit
$Annuity amount$
Length of annuity
yrs
Rate of return
%
Annual growth rate
%
Periodic growth rate
%
Results
The final balance (future value) of your growing annuity is $91,514.60.  Opening balance$0.00 Final balance $91,514.60 Monthly deposit$1,000.00 initially Total deposit $78,682.51 Total return$12,832.09 Number of deposits 72 Last deposit on Aug. 19, 2030
Display...
chart of balances
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