Loading the player...

What is the 'Present Value Of An Annuity'

The present value of an annuity is the current value of future payments from an annuity, given a specified rate of return or discount rate. The annuity's future cash flows are discounted at the discount rate. Thus, the higher the discount rate, the lower the present value of the annuity.

BREAKING DOWN 'Present Value Of An Annuity'

Because of the time value of money concept, receiving money today is worth more than receiving the same amount money in the future because the money today can be invested at a given rate of return. By the same logic, receiving $5,000 today is worth more than getting $1,000 per year for five years. The lump sum invested today is worth more at the end of the five years than the incremental investments of $1,000 each, even if invested at the exact same interest rate.

Example: Calculation of an Ordinary Annuity's Present Value 

The formula for the present value of an ordinary annuity, as opposed to an annuity due, is as follows:

P = PMT x ((1 - (1 / (1 + r) ^ n)) / r)

Where:

P = the present value of an annuity stream

PMT = the dollar amount of each annuity payment

r = the interest rate (also known as the discount rate)

n = the number of periods in which payments will be made

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

Present value of annuity = $50,000 x ((1 - (1 / (1 + 0.06) ^ 25)) / 0.06) = $639,168

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

Note: This formula is for an ordinary annuity where payments are made at the end of the period in question. In the above example, each $50,000 payment would occur at the end of 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, simply multiply the above formula by a factor of (1 + r):

P = PMT x ((1 - (1 / (1 + r) ^ n)) / r) x (1 + r)

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

P = $50,000 x ((1 - (1 / (1 + 0.06) ^ 25)) / 0.06) x (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.

RELATED TERMS
  1. Annuity Table

    An annuity table is a tool for determining the present value ...
  2. Delayed Annuity

    A delayed annuity is an annuity in which the first payment is ...
  3. Annuity in Advance

    Annuity in advance refers to an amount of money that is regularly ...
  4. Secondary Market Annuity – SMA

    A secondary market annuity (SMA) is a transaction in which the ...
  5. Whole Life Annuity

    A Whole Life Annuity is a financial product sold by insurance ...
  6. Income Annuity

    An income annuity is an annuity contract that is designed to ...
Related Articles
  1. Retirement

    Are Annuities Retirement-Only Investments?

    Learn more about why annuities are generally purchased and the way that they can positively and negatively affect an individual preparing for retirement.
  2. Retirement

    Annuities: How To Find The Right One For You

    Fixed, variable and indexed annuities offer different features. Find out which one fits your needs.
  3. Retirement

    5 Mistakes to Avoid When Shopping for Annuities

    Annuities give retirees guaranteed income but they aren't all created equal.
  4. Financial Advisor

    Are Annuities Right for You?

    Annuities are safe and often appealing, but IRAs and 401(k)s offer advantages that annuities typically can’t match, with little additional risk.
  5. Investing

    Why an Annuity May Not Be Right for You

    An annuity, when compared to the many other options available, may not be the best choice.
  6. Retirement

    How a Variable Annuity Works After Retirement

    These investments can provide extra income after you retire. Here’s a guide to when and how you will receive the payout.
  7. Retirement

    Break Out Of Annuity Prison

    Annuities offer security but also lock up your cash. The secondary market could be your key to escape.
  8. Retirement

    How Good a Deal is an Indexed Annuity?

    Indexed annuities are marketed as a compromise between fixed and variable-rate products. But watch the fine print!
Trading Center