 #jsDisabledContent { display:none; } My Account | Register | Help Flag as Inappropriate This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:

Annual effective discount rate

Article Id: WHEBN0018862077
Reproduction Date:

 Title: Annual effective discount rate Author: World Heritage Encyclopedia Language: English Subject: Collection: Interest Rates Publisher: World Heritage Encyclopedia Publication Date:

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.

Contents

• Annual discount rate convertible \,pthly 1
• Business calculations 2
• 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.