Best if printed in landscape.

Calculating Present Value of a Future Payment

The present value of a future payment can be calculated if the amount of the future payment, the time of the future payment, and the discount rate are specified.

• The formula for computing the present value of a future payment is PV = FV/(1+d)^n, where:
  • PV is present value,
  • FV is amount of the future payment,
  • d is the discount rate (expressed as a decimal), and
  • n is the number of time periods until the future payment is received (although it may not be obvious on this web page, n is treated as an exponent to the factor in parenthesis).

This formula may be best understood if the question is "reversed"; that is, how much cash would I have two years from now, for example, if I deposited $10,000 today in a bank account that annually pays 5% interest?

During the first year, the $10,000 would earn $500 interest (10,000 x .05).  This $500 is added to the $10,000 so during the second year, the investment is earning interest on $10,500.  The interest earned the second year would be $525 (10,500 x .05). By the end of the second year, the deposit would have a value of $11,025.  This example illustrates compounded interest; that is, one year's interest will earn interest during the second year.

Expressed as a formula, the first year's interest is calculated as FV = PV(1 + i), where

• FV is the value of the deposit at the end of the first year.
• PV is the value of the original deposit
• i is the interest rate being paid by the bank
• 1 represents that the depositor will receive the original deposit back from the bank (in addition to the interest earned).

Because this deposit will be invested for two years, a second year of interest needs to be incorporated into the formula.  The formula is expanded to FV = PV(1 + i)(1 + i).

Simplifying, the formula is FV = PV(1 + i)^2, where the deposit is invested for two years.

To make the formula more general, the number of time periods also can be expressed as an algebraic variable "n"; the formula then is FV = PV(1 + i)^n.  Restated, the amount or value in the future (FV) is the amount at the present time (PV) increased by the interest rate (i) that will be earned during the time of the investment (n).

This formula can be restated to calculate PV.

FV = PV(1 + i)^n

FV/(1 + i)^n = PV(1 + i)^n/(1 + i)^n

FV/(1 + i)^n = PV

PV = FV/(1 + i)^n

• Example of calculating present value of a future payment. An individual will be paid $50 twenty-one (21) months from now. The individual has an annual discount rate of 6%; that is, the individual feels a payment received one year from now is only worth about 94% of what it would be worth if the payment was received today. Twenty-one months is 1.75 years; because the discount rate is expressed as an annual rate, the time period has to be measured in terms of years. Using the present value formula,

PV = 50/(1+.06)^1.75
PV = $45.15

Also see Time Value of Money and Valuing a Long-term (Capital) Asset.

Last Updated November 3, 2009

Email: David.Saxowsky@ndsu.edu

This material is intended for educational purposes only. It is not a substitute for competent professional advice. Seek appropriate advice for answers to your specific questions.

E-Mail:sswandal@ndsuext.nodak.edu
Published by Agricusiness and Applied Economics
Morrill Room 217
North Dakota State University, Fargo, ND 58105-5636
Phone: (701) 231-7441