Future Value Of Growing Annuity Calculator

What this calculator does

Ordinary savings calculators assume you pay in the same amount forever. Almost nobody does. Salaries rise, rents are reviewed upward, dividends are increased, and sensible savers put a little more away each year than they did the year before. This calculator is built for that: a stream of payments that climbs at a steady rate, and what it all adds up to in the end.

You give it the first payment, the return your money earns, the rate at which the payments themselves grow, and how many periods it runs. It returns the future value of the whole rising stream. Two different rates are at work here, which is what makes this tool distinct: one is what your money earns, and the other is how fast your contributions climb.

"First payment" means the smallest one

The first input is worth pausing on, because misreading it will throw everything off. It asks for the first payment, not a typical one and not an average one. In a growing annuity the first payment is the smallest of the whole series, and every payment after it is larger.

The pattern is straightforward. The second payment is the first multiplied by one plus the growth rate. The third is the second multiplied by the same thing, and so on. So a first payment of 10,000 growing at 5 percent means the series runs 10,000, then 10,500, then 11,025, and by the twenty-fifth payment it has reached 32,251. The formula packages all of that up:

Future value = First payment × [ (1 + return)^periods − (1 + growth)^periods ] ÷ (return − growth)

If you enter what you are currently paying rather than what you started with, you will overstate the whole series. Start at the beginning and let the growth rate do the rest.

How to use it

1. First payment. The amount of the very first contribution, before any increases.
2. Interest rate per period. What the money you have already saved earns each period.
3. Growth rate per period. How much bigger each payment is than the one before, as a percent. If you plan to raise your saving in line with a 5 percent annual pay rise, this is 5.
4. Number of periods. How many payments will be made.

Press Calculate for the future value, or Reset to clear the fields. As always, keep the two rates and the period count on the same clock, so annual periods take annual rates.

A worked example you can check

Say you start by saving 10,000 a year, you increase that by 5 percent each year as your income rises, and the money earns 8 percent a year for 25 years.

• First payment: 10,000. Final, twenty-fifth payment: 32,251
• Total you actually paid in over the 25 years: 477,270.99
• Future value of the growing annuity: 1,154,040.09

So a habit that began at 10,000 a year finishes at just over 1.15 million. Now, the interesting comparison is not against doing nothing. It is against the saver who never increased their contribution at all, and that is where this tool earns its keep.

What escalating your payments actually buys

Run the same 25 years at the same 8 percent return, but with a flat 10,000 every year and no increases. The result is 731,059.40. The escalating saver ends up with 1,154,040.09, which is 422,980.69 more, or roughly 58 percent ahead.

Most calculator sites stop there, and it makes escalation look like magic. It is not, and the honest version is more useful. The escalating saver also paid in a great deal more: 477,270.99 against 250,000, a difference of 227,270.99. So the fair question is not "how much more did I end up with" but "what did those extra contributions turn into". The answer is that 227,270.99 of extra payments produced 422,980.69 of extra final value, which is about 1.86 times itself.

That is still a good deal, and it is a truthful one. It is also slightly less per unit than the flat saver's money achieved, and there is a sound reason: the escalating payments are largest at the end, when they have the least time left to compound. The lesson is not that raising your contributions is free money. It is that raising them works, that the money you add later still roughly doubles at these rates, and that the earlier you can push increases forward, the harder each one works. If your income is going to rise anyway, this calculator tells you what carrying your saving up with it is worth.

When the growth rate meets the return rate

There is one combination this calculator cannot handle, and it is worth knowing why rather than being puzzled by the error. If you set the growth rate exactly equal to the interest rate, the formula's denominator, return minus growth, becomes zero, and dividing by zero has no answer. The tool will report a problem rather than return a figure.

That is a quirk of the shortcut, not of the underlying money. When the two rates are identical there is a separate, simpler formula: the future value is the first payment multiplied by the number of periods, multiplied by one plus the rate raised to the power of one less than the number of periods. With 10,000 a period for 25 periods at 8 percent for both rates, that comes to 1,585,295.18.

Setting growth above the return rate, on the other hand, works normally and the calculator will handle it. It simply describes a stream whose payments are climbing faster than the account is compounding, which is a perfectly sensible thing to model for a few years, though it is an aggressive assumption to carry across decades.

Questions people ask

Do I enter my current payment or my first one?

Your first one, which is the smallest in the series. The calculator grows every later payment for you, so entering your current, larger figure would overstate the whole stream.

What is the difference between the two rates?

The interest rate is what your accumulated savings earn. The growth rate is how much bigger each contribution is than the last. One grows the pot, the other grows the payments.

Why does it fail when both rates are the same?

Because the formula divides by the difference between them, which is zero when they match. That case has its own formula, given in the section above.

What else is a growing annuity?

Any regular payment that rises at a steady rate: escalating commercial rents, pensions linked to a cost of living adjustment, dividends from a company that raises them each year, or salary-linked retirement contributions.

References

The treatment of a stream of periodic payments, and the calculation of what such a stream accumulates to, follows OpenStax's finance text. The growing annuity is the standard extension of that idea to payments that rise at a constant rate each period, the same constant growth assumption used in the dividend models described in the same text, where the relationship between the growth rate and the required return governs the result.

1. OpenStax, Principles of Finance, 8.2 Annuities. https://openstax.org/books/principles-finance/pages/8-2-annuities
2. OpenStax, Principles of Finance, 11.2 Dividend Discount Models (DDMs). https://openstax.org/books/principles-finance/pages/11-2-dividend-discount-models-ddms