World Library  
Flag as Inappropriate
Email this Article

Annual effective discount rate

Article Id: WHEBN0018862077
Reproduction Date:

Title: Annual effective discount rate  
Author: World Heritage Encyclopedia
Language: English
Subject: Cost of electricity by source, Interest rates, Annuity (finance theory), Earnings growth, Depreciation (economics)
Collection: Interest Rates
Publisher: World Heritage Encyclopedia

Annual effective discount rate

The annual effective discount rate expresses the amount of interest paid/earned as a percentage of the balance at the end of the (annual) period. This is in contrast to the effective rate of interest, which expresses the amount of interest as a percentage of the balance at the start of the period. The discount rate is commonly used for U.S. Treasury bills and similar financial instruments.

For example, consider a government bond that sells for $95 and pays $100 in a year's time. The discount rate is

\frac{100-95}{100} = 5.00\%

The interest rate is calculated using 95 as the base

\frac{100-95}{95} = 5.26\%

For every effective interest rate, there is a corresponding effective discount rate, given by

d = \frac{i}{1+i}

or inversely,

i = \frac{d}{1-d}

Given the above equation relating \,d to \,i it follows that

d = \frac{1+i}{1+i} - \frac{1}{1+i}\ = 1-v where v is the discount factor

or equivalently,

v = 1-d

Since \, d = iv ,it can readily be shown that

id = i-d

This relationship has an interesting verbal interpretation. A person can either borrow 1 and repay 1 + i at the end of the period or borrow 1 - d and repay 1 at the end of the period. The expression i - d is the difference in the amount of interest paid. This difference arises because the principal borrowed differs by d. Interest on amount d for one period at rate i is id.


  • Annual discount rate convertible \,pthly 1
  • Business calculations 2
  • See also 3
  • References 4

Annual discount rate convertible \,pthly

A discount rate applied \,p times over equal subintervals of a year is found from the annual effective rate d as

1-d = \left(1-\frac{d^{(p)}}{p}\right)^p

where \,d^{(p)} is called the annual nominal rate of discount convertible \,pthly.

1-d = \exp (-d^{(\infty)})

\,d^{(\infty)}=\delta is the force of interest.

The rate \,d^{(p)} is always bigger than d because the rate of discount convertible pthly is applied in each subinterval to a smaller (already discounted) sum of money. As such, in order to achieve the same total amount of discounting the rate has to be slightly more than 1/pth of the annual rate of discount.

Business calculations

Businesses consider this discount rate when deciding whether to invest profits to buy equipment or whether to deliver the profit to shareholders. In an ideal world, they would buy a piece of equipment if shareholders would get a bigger profit later. The amount of extra profit a shareholder requires to prefer that the company buy the equipment rather than giving them the profit now is based on the shareholder's discount rate. A common way of estimating shareholders' discount rates uses share price data is known as the capital asset pricing model. Businesses normally apply this discount rate by calculating the net present value of the decision.

See also


This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.