Annuity Table

What Is an Annuity Table?

An annuity table is a printed or digital grid that lists precalculated multipliers, called factors, for working out the value of an annuity. An annuity is a stream of equal payments made at regular intervals, such as yearly or monthly. Before spreadsheets and financial calculators became common, students and professionals looked up these factors instead of working through the math each time. Rows usually represent the number of periods, and columns represent interest rates. The factor at the intersection is multiplied by the payment amount to get the answer.

Tables usually come in two main types. A present value table shows what future payments are worth today, using a discount rate. A future value table shows what a series of payments will grow to over time. Both rely on the principle of the time value of money, which holds that a dollar available now is worth more than a dollar received later.

How It Works

The factors come from standard formulas. For an ordinary annuity, where payments occur at the end of each period, the present value factor is:

Present value factor = (1 − (1 + r)^−n) ÷ r

Here r is the interest rate per period and n is the number of periods. The future value factor is:

Future value factor = ((1 + r)^n − 1) ÷ r

An Example

Suppose you expect to receive 1,000 dollars at the end of each year for 5 years, and the relevant rate is 5 percent. The present value table at 5 percent and 5 periods gives a factor of about 4.3295. Multiplying that by 1,000 gives a present value of about 4,329.48 dollars. The future value factor for the same case is about 5.5256, so the same payments would grow to about 5,525.63 dollars by the end of year five.

Advantages and Limitations

Annuity tables are quick to read and show clearly how timing and interest rates affect a payment stream. In insurance, the term can also refer to a mortality table that estimates how long annuitants are likely to live, which insurers use to price lifetime payouts.

The main limitation is coverage. A printed table only includes the rates and periods it lists, so unusual cases require interpolation or a formula. Tables also assume equal payments on a regular schedule. Most investors now use spreadsheet functions such as PV and FV, which calculate the same results for any inputs.