FVIFA Calculator

What this calculator does

FVIFA stands for future value interest factor of an annuity, which is a long name for a small, useful number. Give this calculator a rate and a number of periods and it returns that factor:

FVIFA = [ (1 + rate)^periods − 1 ] ÷ rate

Multiply it by the amount you pay in each period and you have the future value of the whole stream of payments. Like any factor, it carries no currency and no amount, so the same number works for payments of 500 or 500,000. What makes this particular factor pleasant is that it has a plain-language meaning, and once you see it the number stops being abstract.

What the number counts: payments, not money

Here is the reading that makes FVIFA click. The factor is the future value of a payment of exactly 1 per period. So the number it gives you is, quite literally, how many payments' worth you end up holding.

Take 6 percent for 10 periods, where the factor is 13.1808. You made ten payments. You finish with 13.1808 payments' worth of money. The difference, 3.1808, is what the interest built for you, expressed in the only unit that matters to a saver: extra payments you never had to make. At those rates, ten years of saving hands you a bonus worth a little over three years of contributions.

Two things follow, and both are worth carrying around. First, for any positive rate the factor is always larger than the number of periods, since your payments cannot come to less than themselves. Second, the gap between the factor and the period count is a clean measure of how hard the interest is working. Comparing 13.18 against 10 tells you more, faster, than comparing two large currency totals, because the comparison is already scaled.

How to use it

1. Interest rate per period. The rate earned in a single period, as a percent.
2. Number of periods. How many payments are made.

Press Calculate for the factor, or Reset to clear the fields. The result assumes an ordinary annuity, meaning each payment arrives at the end of its period. If your payments land at the start instead, multiply the factor by one plus the rate. Keep the rate and periods on the same clock, so monthly payments need a monthly rate.

A worked example you can check

Take 6 percent a period for 10 periods.

• Factor: (1.06¹⁰ − 1) ÷ 0.06 = 13.1808
• Payments made: 10. Payments' worth held at the end: 13.1808
• Applied to payments of 2,000: 2,000 × 13.1808 = 26,361.59

You can check this against the printed annuity tables that finance and accounting texts have carried for decades. OpenStax's accounting text works an example at 12 percent for 15 periods, where the published factor is 37.280, and multiplying it by contributions of 10,000 gives a future value of about 372,800. Run those same inputs here and the calculator returns 37.280 as well. The tool is computing what the tables used to list.

FVIFA and the plain future value factor are siblings

There is a near-identical tool on this site, the future value factor calculator, which asks for exactly the same two inputs and returns a different number. Knowing which one you want takes one question: is this a single sum, or a series of payments?

• One amount, sitting there growing. That is the plain future value factor, (1 + rate)^periods. At 6 percent for 10 periods it is 1.7908.
• The same amount paid in every period. That is FVIFA, 13.1808 under the same conditions.

The two are not just related, they are built from each other. Take the plain factor, subtract one, divide by the rate, and you have FVIFA: (1.7908 − 1) ÷ 0.06 = 13.1808. That is the arithmetic of stacking up a series of single sums, each one compounding for a different length of time, and collapsing them into one figure.

So the sizes will not be comparable and are not meant to be. One tells you what a lump becomes, a number a little above 1. The other tells you how many payments' worth a habit becomes, a number that climbs well past your period count. Reaching for the wrong one will not be subtle: 1.7908 and 13.1808 answer completely different questions.

Questions people ask

What does the FVIFA number actually mean?

It is the future value of 1 paid in per period, so it tells you how many payments' worth you finish with. A factor of 13.18 on 10 payments means interest added a little over three payments' worth.

How do I turn it into money?

Multiply it by your payment per period. The factor is currency-free, so the same one works for any payment size.

How is this different from the future value factor?

That one is for a single sum left to grow. This one is for a series of equal payments. They share inputs but answer different questions, and FVIFA is always the much larger number.

What if my payments are at the start of each period?

Multiply the factor by one plus the rate. This calculator assumes an ordinary annuity, with payments at the end of each period.

References

The annuity factor, the multiplier applied to a periodic cash flow to obtain the future value of a stream of equal payments, is set out with worked examples and published factor tables in OpenStax's accounting texts, whose future value of an ordinary annuity table gives 37.280 at 15 periods and 12 percent. The underlying compounding factor from which it is built is described in OpenStax's finance text.

1. OpenStax, Principles of Accounting, Volume 2: Managerial Accounting, 11.3 Explain the Time Value of Money and Calculate Present and Future Values of Lump Sums and Annuities. https://openstax.org/books/principles-managerial-accounting/pages/11-3-explain-the-time-value-of-money-and-calculate-present-and-future-values-of-lump-sums-and-annuities
2. OpenStax, Principles of Accounting, Volume 1: Financial Accounting, Appendix B: Time Value of Money. https://openstax.org/books/principles-financial-accounting/pages/b-time-value-of-money