# Annuity Table Explained: Calculate Present Value With Examples and Formulas

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## What Is an Annuity Table?

An annuity table is crucial for calculating the present value of structured payment series, typically used by financial professionals like accountants and actuaries. This article offers a detailed guide on leveraging annuity tables, complete with practical examples and formulas to enhance your understanding of present value calculations.  

### Key Takeaways

*   An annuity table is a tool used to calculate the present value of future annuity payments using a discount rate.  
    
*   The present value of an annuity helps determine if an individual should take a lump-sum today or opt for future annuity payments.  
    
*   Financial professionals utilize annuity tables to simplify complex calculations in determining the value of annuities.

#### What Is An Annuity?

## Understanding the Mechanics of Annuity Tables

An annuity table gives a factor, based on time and a discount rate, to calculate an annuity's present value. For example, an annuity 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%.

> **Important**
>
> According to the concept of the time value of money, receiving a lump-sum payment in the present is worth more than receiving the same sum in the future.

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](https://www.investopedia.com/articles/investing/042016/5-best-ways-earn-interest.asp) 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.

## Calculating Present Value With an Annuity Table

### Key Formulas for Present Value of Annuities

The formula for the present value of an [ordinary annuity](https://www.investopedia.com/terms/o/ordinaryannuity.asp), as opposed to an [annuity due](https://www.investopedia.com/terms/a/annuitydue.asp), is as follows:

$\begin{aligned}&\text{P} =\text{PMT}\times\frac{ 1 - (1 + r) ^ -n}{r}\\&\textbf{where:}\\&\text{P} = \text{Present value of an annuity stream}\\&\text{PMT} =\text{Dollar amount of each annuity payment}\\&r = \text{Interest rate (also known as the discount rate)}\\&n = \text{Number of periods in which payments will be made}\end{aligned}$

Assume an individual has an opportunity to receive an annuity that 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:

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

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, [this formula is for an ordinary annuity](https://www.investopedia.com/ask/answers/060915/what-are-differences-between-annuity-derivation-and-perpetuity-derivation-time-value-money.asp), 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 of an annuity due, multiply the above formula by a factor of (1 + r):

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

If the above example were of an annuity due, its value would be:

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

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

### How to Use An Annuity Table for Present Value Calculations

Instead of using the formulas, you can use an annuity table. It simplifies the math by providing a factor for the formula's second half. 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 depends on the interest rate and the number of payment periods. The interest rate is commonly depicted across the top row. 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. Multiply that factor by the annuity payment to get the present value.

Below is an example 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.

## What Is an Annuity?

An annuity is an insurance contract that provides an income stream, typically during retirement. An annuity may be [fixed](https://www.investopedia.com/terms/f/fixedannuity.asp), [variable](https://www.investopedia.com/terms/v/variableannuity.asp), or [indexed](https://www.investopedia.com/terms/i/indexedannuity.asp). There are two phases: first, the [accumulation (savings) phase](https://www.investopedia.com/terms/a/accumulationphase.asp), then, the [payout (income) phase](https://www.investopedia.com/terms/p/payoutphase.asp). The payout may be [immediate](https://www.investopedia.com/terms/i/immediatepaymentannuity.asp) or [deferred](https://www.investopedia.com/terms/d/deferredannuity.asp).  

## What Is the Difference Between an Ordinary Annuity and an Annuity Due?

An ordinary annuity generates payments at the end of the annuity period, while an annuity due is an annuity with the payment expected or paid at the start of the payment period.

## Can a Lottery Winner Use an Annuity Table?

A lottery winner could use an annuity table to determine whether it makes more financial sense to take their lottery winnings as a lump-sum payment today, or as a series of payments over many years. However, [lottery winnings](https://www.investopedia.com/managing-wealth/winning-jackpot-dream-nightmare/) are a rare form of an annuity. More commonly, annuities are a type of investment used to provide individuals with a steady income in retirement.

## Summary: The Importance of Annuity Tables

An annuity table empowers financial professionals to easily calculate the present value of an annuity by providing pre-calculated factors for various interest rates and periods. It simplifies complex mathematical conversions to help determine how much future annuity payments are worth today, ensuring individuals or organizations can make informed financial decisions. By understanding the discount rate and number of periods, users can accurately compare annuity offers with lump-sum payment options.