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. Delayed Annuity

    A delayed annuity is an annuity in which the first payment is ...
  2. Whole Life Annuity

    A Whole Life Annuity is a financial product sold by insurance ...
  3. Valuation Period

    The time between the end of the business day of the first business ...
  4. Income Annuity

    An income annuity is an annuity contract that is designed to ...
  5. Life Annuity

    A life annuity is an insurance product that features a predetermined ...
  6. Annuity Certain

    Annuity certain refers to an annuity contract that provides a ...
Related Articles
  1. Retirement

    Present and Future Value of Annuities

    Do you want to invest in annuities that get you a series of payments over a period of time. Here's everything you need to account for when calculating the present and future value of annuities.
  2. Investing

    DIY Annuities: What You Need to Know

    Annuities are attractive because they can give you a stream of income, but they can be tricky to buy.
  3. Financial Advisor

    Annuities: A Good Option in Turbulent Times?

    Annuities can be an enticing option as Americans near retirement, but there are several reasons to be wary of them.
  4. Investing

    Should You Buy an Annuity?

    There are both pros and cons of buying an annuity, so do your due diligence before investing in one.
  5. Retirement

    5 Mistakes to Avoid When Shopping for Annuities

    Annuities give retirees guaranteed income but they aren't all created equal.
  6. 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.
  7. 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.
  8. Financial Advisor

    Advising FAs: Explaining Annuities to a Client

    Conceptually speaking, annuities can be thought of as a reverse form of life insurance.
  9. Investing

    Introduction to Annuities

    Everything you need to know about annuities.
  10. Retirement

    Watch Your Back In The Annuity Game

    Find out how to get the upper hand when dealing with this payout challenge.
Hot Definitions
  1. Yield Curve

    A yield curve is a line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but ...
  2. Portfolio

    A portfolio is a grouping of financial assets such as stocks, bonds and cash equivalents, also their mutual, exchange-traded ...
  3. Gross Profit

    Gross profit is the profit a company makes after deducting the costs of making and selling its products, or the costs of ...
  4. Diversification

    Diversification is the strategy of investing in a variety of securities in order to lower the risk involved with putting ...
  5. Intrinsic Value

    Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, and may differ ...
  6. Current Assets

    Current assets is a balance sheet item that represents the value of all assets that can reasonably expected to be converted ...
Trading Center