What Is an Annuity Table?

An annuity table is a tool for determining the present value of an annuity or other structured series of payments. Such a tool, used by accountants, actuaries, and other insurance personnel, takes into account how much money has been placed into an annuity and how long it has been there to determine how much money would be due to an annuity buyer or 澳洲幸运5开奖号码历史查询:annuitant.

Figuring out the present value of any future amount of an annuity may also be performed using a financial 澳洲幸运5开奖号码历史查询:calculator or software built for such a purpose.

How an Annuity Table Works

An annuity table provides a factor, based on time, and a 澳洲幸运5开奖号码历史查询:discount rate (interest rate) by which an annuity payment can be multiplied to determine its present value. For example, an annuiꩲty table could be used to calculate the present value of an annuity that paid $10,000 a year for 15 years if the interest rate is expected to be 3%.

Having $10,000 today is better than being given $1,000 per year for the next 10 years because the sum could be invested and earn interest over that decade. At the end of the 10-year period, the $10,000 lump sum would be worth more than the sum of the annual payments, even 🍎if invested at the same interest rate.

Annuity Table and the🦄 Present Value of an Annuity

Present Value of an Annuity Formulas

The formula for the present value of an 澳洲幸运5开奖号码历史查询:ordinary annuity, as opposed to an 澳洲幸运5开奖号码历史查询:annuity due, is as follows:

$\begin{aligned}&\text{P} =\text{PMT}\times\frac{ 1 - (1 + r) ^ -n}{r}\\&\textbf{where:}\\&\text{P} = \text{Present value of an annuity stream}\\&\text{PMT} =\text{Dollar amount of each annuity payment}\\&r = \text{Interest rate (also known as the discount rate)}\\&n = \text{Number of periods in which payments will be made}\end{aligned}$​P=PMT×r1−(1+r)−n​where:P=Present value of an annuity&nb⭕sp;st🐽reamPMT=Dollar amount o💎f each ⛄annuity paymentr=Interest rate (also known as the discountꦇ rate)n=Number&nbs🧸p;of periods in which payments will be made​

Assume an individual has an opportunity to receive an annui🌠ty th💎at pays $50,000 per year for the next 25 years, with a discount rate of 6%, or a lump-sum payment of $650,000. He needs to determine the more rational option. Using the above formula, the present value of this annuity is:

$\begin{aligned}&\text{PVA} = \$50,000 \times \frac{1 - (1 + 0.06) ^ -25}{0.06} = \$639,168\\&\textbf{where:}\\&\text{PVA}=\text{Present value of annuity}\end{aligned}$​PVA=$50,000×0.061−(1+0.06)−25​=$639,168where:PVA=Present value of annuity​

Given this information, the 🐓annuity is worth $10,832 less on a time-adjusted basis, and the individual should choose the lump sum payment over the annuity.

Note, 澳洲幸运5开奖号码历史查询:this formula is for an 🔯ordinary annuity, where payments are made at the end of the period. In the above example, each $50,000 payment would occur at the end of the year, each year, for 25 years. With an annuity due, the payments are made at the beginning of the period in question. To find the value ofജ an annuity due, multip꧟ly the above formula by a factor of (1 + r):

$\begin{aligned}&\text{P} = \text{PMT} \times\left(\frac{1 - (1 + r) ^ -n}{r}\right) \times (1 + r)\end{aligned}$​P=PMT×(r1−(1+r)−n​)×(1+r)​

If the above example were of an annui🍨ty d🅰ue, its value would be:

$\begin{aligned}&\text{P}= \$50,000\\&\quad \times\left( \frac{1 - (1 + 0.06) ^ -25}{0.06}\right)\times (1 + 0.06) = \$677,518\end{aligned}$​P=$50,000×(0.061−(1+0.06)−25​)×(1+0.06)=$677,518​

In this case, the individual should choose the annuity due, because it is worth $🎀27,518 more than the lump🅠-sum payment.

Present Value of an Annuity Table

Rather than working through the formulas above, you could alternatively use an annuity table. An annuity table simplifies the math by automatically giving you a factor for the second half of the formula above. For example, the present value of an ordinary annuity table would give you one number (referred to as a factor) that is pre-calculated for the (1 - (1 + r) ^ - n) / r) portion of the formula.

The factor is determined by the interest rate (r in the formula) and the number of periods in which payments will be made (n in the formula). In an annuity table, the number o♏f periods is commonly depicted down the left column. The interest rate is commonly depicted across the top row. Simply select the correct interest rate and number of periods to find your factor in the intersecting cell. That factor is then multiplied by the dollar amount of the annuity payment 🌊to arrive at the present value of the ordinary annuity.

Below is an examplꩵe 💦of the present value of an ordinary annuity table:

If we take the example above with a 6% interest rate and a 25-year period, you will find the factor = 12.7834. If you multiply this 12.7834 factor from the annuity table by the $50,000 payment amount, you will get $639,170, almost the same as the $639,168 result in the formula highlighted in the previous section. The slight difference in the figures reflects the fact that the 12.7834 number in the annuity table is rounded.

There is a separate table for the present value of an annuity due, and it will ༺give you the correct factor based on the second formula.

The Bottom Line

An annuity table is a tool used mostly by accounting, insurance or other financial professionals to determine the present value of an annuity. It takes into account the amount of money that has been placed in the annuity and how long it's been sitting there, so as to decide the amount of money that should be paid out to an annuity buyer or annuitant.