What Is an Annuity Factor?

Many people encounter the idea of annuities as related to retirement, investments and insurance products. In all cases, annuities pay out at regular intervals for a given timeframe and understanding the annuity factor is an important part of calculating how annuities will pay out and what actions you need to take.

There are different types of annuities, but at base, an annuity is a series of cash flows that pay out at regular intervals, the Association of Corporate Treasurers explains. This is a pretty broad definition, but examples of annuities are not hard to come by. Paychecks for those who work regular hours or are salaried are a type of annuity, typically paid in equal amounts every two weeks.

However, most often, annuities are discussed in the context of retirement. Annuity.org explains that, in this context, an annuity is an insurance contract that pays out fixed amounts for a set number of years or for a person's remaining lifetime. This sort of income stream typically supplements other retirement income such as Social Security payments or retirement plan (e.g. 401(k) or IRA) payouts.

Annuities work by being funded in a lump or over time and accumulating interest at the advertised rate, with payments starting immediately or at a future date. The latter are called deferred annuities, and they are broken into two phases: the accumulation phase, during which you are paying into the plan and the money is earning interest, and the annuitization phase, during which the money is being paid out.

The time value of money is an important concept for understanding annuities and annuity factors. The Corporate Finance Institute explains that having money in hand now is more valuable than the promise of money in the future. This is because the money you have now can be invested and earn a return, so the loss in value over time is how much you could have made if you'd invested that money. Related concepts worth understanding are the present and future values of money.

The future value of money is what you would get at the end of the period if you invested a given sum at a certain interest rate for a set amount of time. The formula for future value (FV) is FV = PV x (1 + (r/n))^(n*t), where PV is the present value of the money, r is the interest rate, n is the number of compounding periods in the year and t is the number of years.

For example, if you invested ​$10,000​ at a rate of ​5 percent​, compounded annually, for ​10 years​, you would calculate ​FV = $10,000 x (1 + (0.05/1))^(1*10) = $16,289​. So if someone offered you a choice between getting ​$10,000​ now or ​$15,000​ in the future, you could be tempted by having that money now, or, conversely, by a larger sum in the future. This future value calculation lets you easily compare these choices. Assuming you can for sure get that rate of return, taking the smaller payment now is the better choice, as you will get ​$1,289​ additional funds by going this route. If you can't be sure of that rate of return and are sure you will actually receive the future payment, then that's the better option.

​Consider also:​ Aggregation Rules on Annuities

This formula can also be used to calculate what money you receive in the future would be worth today. The formula is identical, except you divide the future value instead of multiplying by the present value. In our example, the present value of that offered ​$15,000​ is ​PV = $15,000 / (1 + (0.05/1))^(1*10) = $9,208​. This fits our understanding that taking the ​$10,000​ now and investing it at ​5 percent​ is the better option, because that future ​$15,000​ is worth less today than the ​$10,000​ we have in hand.

Of course, since we're talking about the value of money changing over time, you must be thinking about the role of inflation. While this is relevant, there's not a neat way to predict that. However, you should definitely account for inflation when comparing present and future values.

In the example, the difference over the course of 10 years is only ​$1,289​. According to the U.S. Bureau of Labor Statistics Inflation Calculator, ​$10,000​ in September 2011 has the same buying power as ​$12,090.05​ in September 2021. That's a difference of ​$2,090,​ which is greater than the theoretical gain in the example. If we expect inflation to stay roughly the same for the next decade, then taking that future ​$15,000​ could be smarter after all.

Finally, the annuity factor itself is a sort of shortcut between present value and future value that can be used to calculate either. If you examine the present/future value formula, the big messy bit actually only depends on the interest rate and the number of years if we assume that it's compounded once a year. That means that it's a constant for any given interest rate and number of periods. So we could have arrived at the above calculated amounts by multiplying PV by a known constant. You could call this number the present value interest factor.

That is how annuity factors work. It uses the discount rate (similar to an interest rate) and the length of time (here represented by the number of payments made) to come up with a constant you can use to derive present and future values.

When working with annuities, you typically want to know the present value of the payments you will be receiving over the life of the annuity. For example, if you expect to receive ​$1,000​ a year for 10 years at a discount rate of ​5 percent,​ how much would those payments be worth if you had all that money in hand today? This means you need to know the present value interest factor of an annuity, or PVIFA. The formula for this is PVIFA = (1 - (1 + r)^-n) / r.

It looks pretty similar to the factors in the formulas above. The PVIFA for ​5 percent​ interest (r) and ​10​ payments (n) is ​7.7217​. Then, we multiply this by our ​$1,000​ cash flow to obtain ​$7,722​. It, therefore, seems that what would have been ​$10,000​ in hand now is only worth ​$7,722​ when paid out over time. In this sense, higher discount rates make for lower present values.

Because annuity rates are constant, you can quickly arrive at these values by using annuity tables. There are separate present value interest factors and future value interest factors, so make sure you have the correct type of table. Then look for the intersection of the rate and the number of periods or payments.