Growing Annuity Calculator

The growing annuity calculator estimates the ending value of payments that rise or fall by a steady growth rate. It is built for situations where a level-payment annuity is too simple: retirement deposits that increase with salary, lease payments with annual escalators, tuition withdrawals that follow inflation, or planned contributions that grow as cash flow improves. Enter the first payment, annual return, annual payment growth, payment frequency, timing, and any opening balance. The result shows the final balance, total payments, investment return, number of payments, and the periodic payment growth rate used by the calculation.

Informational, not financial advice. A growing annuity is a mathematical model, not a promise that an account, insurer, tenant, or borrower will behave exactly as planned.

How this calculator matches the inputs

The calculator first converts the schedule into payment periods. Six years with monthly payments becomes 72 payments because the code rounds years multiplied by payments per year. The annual return is treated as a nominal rate divided by the payment frequency. The annual payment growth is converted differently: it is transformed into the effective growth per payment period, so a 3% annual growth assumption becomes about 0.2466% per month, not 3% every month.

Payment timing changes the future value. If you select end of period, the first payment is invested after the first period’s growth. If you select beginning, the calculation multiplies the payment stream by one extra period of return. The opening balance is separate; it compounds for the full number of periods and then is added to the future value of the growing payment stream.

Use this calculator beside the broader annuity calculator, the present value calculator, and the future value calculator to compare the same cash-flow idea from different directions. If you are comparing level payments, the present value annuity calculator and future value annuity calculator are closer fits.

Formula used

For an ordinary growing annuity, where payments are made at the end of each period, the payment stream is:

$\text{future value of payments} = P \times \frac{(1+r)^n - (1+g)^n}{r-g}$

For a growing annuity due, where payments are made at the beginning of each period, the calculator multiplies that payment value by one extra period of return:

$\text{future value of payments due} = P \times \frac{(1+r)^n - (1+g)^n}{r-g} \times (1+r)$

The optional opening balance is compounded separately:

$\text{opening balance future value} = B \times (1+r)^n$

The final balance is the sum of both pieces:

$\text{final balance} = \text{opening balance future value} + \text{future value of payments}$

When the periodic return and periodic growth are effectively equal, the calculator switches to this equivalent formula:

$\text{future value of payments} = P \times n \times (1+r)^{n-1} \times \text{timing factor}$

Here P is the first payment, r is the periodic return, g is the periodic growth rate, n is the rounded number of payments, B is the opening balance, and the timing factor is one for end-of-period payments or one plus r for beginning payments.

Worked example matching the default calculator

The default scenario uses a first payment of $1,000, a 6-year schedule, a 5% annual return, 3% annual payment growth, monthly payments, beginning timing, and a $0 opening balance.

The number of payments is:

$6 \times 12 = 72$

The periodic return is:

$5\% \div 12 = 0.4166667\%$

The periodic growth rate is converted from the annual growth assumption:

$g = (1 + 3\%)^{1/12} - 1 = 0.24662698\%$

Using the annuity-due formula, the payment stream grows to $91,514.60. The total of all growing payments is $78,682.51, so the investment return shown by the calculator is $12,832.09. There is no opening balance in the default case, so the final balance is also $91,514.60.

When a growing annuity is useful

Use a growing annuity when the payment pattern is the point of the analysis. A 25-year-old increasing retirement contributions as pay rises, a landlord modeling annual rent escalators, or a nonprofit planning recurring grants that keep pace with inflation all need a payment stream that changes over time. The model is also useful for stress testing. You can hold the first payment constant, raise or lower the growth rate, and see how much of the ending value depends on later, larger payments.

The calculator is not the best choice when payments are irregular, have a hard cap, skip months, or change according to a table rather than a constant rate. In those cases, a spreadsheet cash-flow model can show each payment explicitly. It also does not estimate present value, insurer pricing, mortality credits, surrender charges, or taxes. For variable annuity contracts and other insurance products, read the contract terms and compare the projection with fee and risk disclosures.

Caveats and interpretation

Small differences in the return and growth assumptions can create large changes over many periods. If the return is only slightly higher than payment growth, the denominator in the formula is small, so the result can be sensitive. If the payment growth rate is higher than the investment return, later payments may dominate the final value; that may be realistic for salary-linked deposits but less realistic for fixed budgets.

Remember that the result is nominal unless your inputs are inflation-adjusted. A 5% return and 3% payment growth do not mean purchasing power grows at 5%. Fees, taxes, late deposits, and investment losses can reduce the final balance. Use this page for transparent scenario math, then compare the answer with your broader saving, risk, and liquidity plan.

Sources

• SEC Investor.gov, Annuities — investor-facing overview of annuity products and risks.