Loading the player...

What is the 'Present Value Of An Annuity'

The present value of an annuity is the current value of a set of cash flows in the future, given a specified rate of return or discount rate. The future cash flows of the annuity 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 financial concept known as the time value of money, 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.

Ordinary Annuity Present Value Example Calculation

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)


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 an opportunity to receive an annuity that pays $50,000 per year for the next 25 years, with discount rate of 6% or a lump sum payment of $650,000, 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 and 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 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, simply multiply the above formula by a factor of (1 + r):

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

Were the above example an annuity due, it's 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.

  1. Future Value Of An Annuity

    The value of a group of payments at a specified date in the future. ...
  2. Ordinary Annuity

    A series of equal payments made at the end of each period over ...
  3. Annuity Due

    An annuity whose payment is to be made immediately, rather than ...
  4. Delayed Annuity

    An annuity in which the first payment is paid at a later date ...
  5. Annuity Table

    A method for determining the present value of a structured series ...
  6. Annuity

    A financial product that pays out a fixed stream of payments ...
Related Articles
  1. Retirement

    How to Calculate the Value of Annuities

    Here's everything you need to account for when calculating the present and future value of annuities.
  2. Investing

    Calculating the Present Value of an Annuity

    The present value of an annuity is the current, lump sum value of periodic future payments as calculated using a specific rate.
  3. 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.
  4. 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.
  5. 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.
  6. Retirement

    How a Fixed Annuity Works After Retirement

    These popular investments can provide a steady stream of income during your retirement years. Here are the details.
  7. Investing

    What's an Ordinary Annuity?

    An ordinary annuity is a series of equal payments made at the end of each period over a fixed amount of time.
  8. Retirement

    5 Mistakes to Avoid When Shopping for Annuities

    Annuities give retirees guaranteed income but they aren't all created equal.
  9. Retirement

    Guaranteed Retirement Income In Any Market

    By laddering annuities, you can be sure you'll have income no matter what the market does.
  10. Retirement

    Who Benefits From Retirement Annuities

    Annuities guarantee some degree of fixed income in retirement. But is the security worth the fees and less favorable tax treatment? How to decide.
  1. What exact information is included in the interest rate when calculating the present ...

    Find out what the interest rate of an annuity means in the context of the present value calculation, including an explanation ... Read Answer >>
  2. For what types of financial instruments would I want to calculate the present value ...

    Learn about the types of financial instruments the present value of an annuity calculation is most useful for, including ... Read Answer >>
  3. Why would I need to calculate the present value of an annuity?

    Find out what information is needed to calculate the present value of an annuity, including an example of the present value ... Read Answer >>
  4. How do I calculate the future value of an annuity?

    Find out how to calculate the future value of an ordinary annuity or an annuity due, including how the power of compounding ... Read Answer >>
  5. What is the difference between the present value of an annuity and the future value ...

    Find out about the difference between the future value and present value of a fixed annuity, including how to use these calculations ... Read Answer >>
Hot Definitions
  1. Graduate Record Examination - GRE

    A standardized exam used to measure one's aptitude for abstract thinking in the areas of analytical writing, mathematics ...
  2. Graduate Management Admission Test - GMAT

    A standardized test intended to measure a test taker's aptitude in mathematics and the English language. The GMAT is most ...
  3. Magna Cum Laude

    An academic level of distinction used by educational institutions to signify an academic degree which was received "with ...
  4. Cover Letter

    A written document submitted with a job application explaining the applicant's credentials and interest in the open position. ...
  5. 403(b) Plan

    A retirement plan for certain employees of public schools, tax-exempt organizations and certain ministers. Generally, retirement ...
  6. Master Of Business Administration - MBA

    A graduate degree achieved at a university or college that provides theoretical and practical training to help graduates ...
Trading Center