Pamela Peterson Drake, James Madison University
T
ransactions on securities do not often occur at the end of a compounding period. Because of this,
we need to be able to calculate what is earned up to a transaction date. More specifically, we
need to be able to calculate interest for a settlement date, which is three business days from the actual
transaction date.
Accrued interest is interest on a security that has been earned up until the transaction date, but not yet
paid. For example, if an investor buys a bond mid-way between two coupon payments on the bond, the
seller is generally compensated for any earned but not paid interest. The seller is compensated through
the bond’s price, which includes the present value of the bond to the date of sale and any accrued
interest. A bond’s quote that does not include accrued interest is the clean price; a bond quote that
includes accrued interest is the dirty price.
The process of determining the accrued interest requires the following information:



Settlement date (that is, the trade date or the date of the valuation)
Date of the most recent coupon payment
Number of dates for which interest is accrued
Another important piece of information is the day count convention, as I show in Table 1.
Table 1 Day count conventions
Day count
convention
Actual/Actual
Also known as
What it means
Examples of uses
ISMA-99 Normal
Euro bonds
30/360
German
U.S.
Actual number of days in a
month/Actual number of days in a
coupon period.
Each month has 30 days and each year
has 365 days
Actual/365
English
Actual number of days and each year
has 365 days (ignores leap years)
U.S. Treasury bonds
U.K. Gilt Edged Market
Actual/360
French
Actual number of days, but assumes
that there are 360 days in a year
U.S. Treasury bills
Commercial paper
French money markets
U.S. corporate bonds
U.S. agency issues
In theory, accrued interest is the portion of the coupon period that has passed based on the settlement
date, multiplied by the coupon amount:1
Accrued interest
1
oupon
(
a s since ost recent coupon
)
a s in coupon period
The settlement date is a specified number of days after a trade takes place, at which securities must be
delivered. For purposes of valuation, we use the settlement date as the trade date.
However, the day count that is used in the numerator and denominator are based on the day count
convention used for that security. If A is the accrued interest, N the number of interest-bearing days up
to the settlement, and C the coupon amount, in dollar terms, the accrued interest is:
Day count
convention
30/360
Number of
days in a year
360
A=C
Actual/365
365
A=C
Actual/360
360
A=C
Formula
For any convention requiring the actual days, the accrued interest is A = C × (
number of days in coupon period and N is the number of days since the last coupon.
), where Y is the
If a bond trades ex-coupon, the buyer does not receive the forthcoming coupon; the seller received the
entire coupon. Bonds that trade in this manner generally specify that if a trade date is close to the
coupon date, the bond sells without the coupon, and the seller receives the entire coupon.
Microsoft Excel
We can calculate accrued interest using a spreadsheet function. In Excel, the appropriate function is
ACCRINT, which requires specifying:
ACCRINT(issue,first_interest,settlement,rate,par,frequency,basis,calc_method)
where
Argument
issue
first_interest
settlement
rate
par
frequency
basis
calc_method
Description
The issue date for the security
The date of the first interest paid on the security
Transaction date
Coupon rate
Face value
Frequency of interest payments
Day count convention:
1
30/360
2
Actual/Actual
3
Actual/365
4
European 30/360
1
Accrued interest is the amount since the
issuance to settlement
0
Accrued interest is the amount since the
first_interest
The result of ACCRINT is the total accrued interest earned from the issue date to the settlement date.
For example, using a bond with a 4% coupon, maturity date of 1/5/2016, issue date of 12/9/2010, and a
first coupon date of 7/5/2011, the result of ACCRINT for the following dates is:
Settlement
date
12/10/2010
12/11/2010
12/12/2010
12/13/2010
12/14/2010
12/15/2010
12/16/2010
12/17/2010
Price
$95.568
$95.570
$95.572
$95.574
$95.576
$95.579
$95.581
$95.583
Accrued
interest
$0.011
$0.022
$0.033
$0.044
$0.056
$0.067
$0.078
$0.089
The accrued interest provided by the ACCRINT function is the accumulated interest since the security
was issued. This would be relevant if you need to account for the taxable portion of the accrued interest
for a given tax year.
The owner of an original issue discount bond, more commonly a zero coupon bond, is taxed on the
amount of accrued interest during the tax year. Excel has a specific function for zero coupon bonds,
ACCRINTM. The arguments for this function are:
ACCRINTM(issue,maturity,rate,par,basis)
as defined previously. ACCRINTM calculates the amount of the accrued interest over the life of the
bond.
In a bond transaction, ou would be ore interested in the accrued interest that is part of the bond’s
price when quoted with interest, where this interest is from the most recent coupon payment date. To
calculate this you need to calculate the proportion of the coupon period, and then apply it against the
period’s coupon:2
Accrued interest
oupon pa
ent
u ber of da s since the last coupon
u ber of da s between coupons
In Excel, you can use the day counting functions, COUPDAYBS and COUPDAYS, for the number of days
since the last coupon and the number of days between coupons, respectively. The information needed
for these counting functions is the settlement date, the maturity date, the frequency of coupons in a
year, and the day count basis.
For this 4% coupon bond issued 12/9/2010, each coupon payment using a 100 par value is $2. The
accrued interest under the four different day conventions used in Excel, from the first coupon payment
on is the following:
2
An alternative is to use the result of ACCRINT and then subtract the coupons already paid, using
COUPNUM to determine the number of coupons between two dates.
Date
1/5/2011
1/6/2011
1/7/2011
1/8/2011
1/9/2011
1/10/2011
1/11/2011
1/12/2011
1/13/2011
1/14/2011
1/15/2011
1/16/2011
1/17/2011
US 30/360
Actual/Actual Actual/360 Actual/365
$0.0000
$0.0111
$0.0222
$0.0333
$0.0444
$0.0556
$0.0667
$0.0778
$0.0889
$0.1000
$0.1111
$0.1222
$0.1333
$0.0000
$0.0110
$0.0221
$0.0331
$0.0442
$0.0552
$0.0663
$0.0773
$0.0884
$0.0994
$0.1105
$0.1215
$0.1326
$0.0000
$0.0111
$0.0222
$0.0333
$0.0444
$0.0556
$0.0667
$0.0778
$0.0889
$0.1000
$0.1111
$0.1222
$0.1333
$0.0000
$0.0110
$0.0219
$0.0329
$0.0438
$0.0548
$0.0658
$0.0767
$0.0877
$0.0986
$0.1096
$0.1205
$0.1315
European
30/360
$0.0000
$0.0111
$0.0222
$0.0333
$0.0444
$0.0556
$0.0667
$0.0778
$0.0889
$0.1000
$0.1111
$0.1222
$0.1333
As you can see, there is a slight difference in the accrued interest, depending on the convention. As we
would expect, the smallest amount of accrued interest is from using the Actual/365.
Accounting and accrued interest
Accrued interest for accounting purposes represents interest that has been earned, but not paid or
received (depending on which side of the transaction the party is on). This is the result of using the
accrual basis for accounting. Therefore, accounting definition is a bit different than the definition we
use for a bond.
For example, suppose a company buys a bond November 1, 2011 that pays 6% interest May 1st and
November 1st each year until maturity November 1, 2015. The accrued interest, which would be a shortterm asset, is interest receivable for the interest earned in November and December. For a 6% bond,
that is 6% x 0.5 × 100 × 1/3 = $1 for every $100 face value. For the company that sold the bond, there
would be an interest payable of $1 for every $100 face value.