- Accrued interest
In

finance ,**accrued interest**is theinterest that has accumulated since theinvestment , or since the previous interest payment if there has been one already. For afinancial instrument such as a bond, interest is calculated and paid in set intervals.**Formula**The primary formula for calculating the interest accrued in a given period is:

$I\_A\; =\; T\; imes\; P\; imes\; R$

where $I\_A$ is the accrued interest, $T$ is the fraction of the year, $P$ is the principal, and $R$ is the annualized interest rate.

$T$ is calculated as follows:

$T\; =\; frac\{D\_P\}\{D\_Y\}$

where $D\_P$ is the number of days in the period, and $D\_Y$ is the number of days in the year.

A

compounding instrument adds the previously accrued interest to the principal each period.The main variables that affect the calculation are the period between interest payments and the day count convention used to determine the fraction of year, and the date rolling convention in use..

**Day count conventions**Common day count conventions that affect the accrued interest calculation are:

* actual/360 (days per month, days per year)Each month is treated normally and the year is assumed to be 360 days e.g. in a period from February 1, 2005 to April 1, 2005 T is considered to be 59 days divided by 360.* 30/360Each month is treated as having 30 days, so a period from February 1, 2005 to April 1, 2005 is considered to be 60 days. The year is considered to have 360 days. This convention is frequently chosen for ease of calculation: the payments tend to be regular and at predictable amounts.

* actual/365Each month is treated normally, and the year is assumed to have 365 days, regardless of leap year status. For example, a period from February 1, 2005 to April 1, 2005 is considered to be 59 days. This convention results in periods having slightly different lengths.

* actual/actual (ACT/ACT) - (1)Each month is treated normally, and the year has the usual number of days. For example, a period from February 1, 2005 to April 1, 2005 is considered to be 59 days. In this convention leap years do affect the final result.

* actual/actual (ACT/ACT) - (2)Each month is treated normally, and the year is the number of days in the current coupon period multiplied by the number of coupons in a year e.g. if the coupon is payable 1 February and August then on April 1, 2005 the days in the year is 362 i.e. 181 (the number of days between 1 February and 1 August 2005) x 2 (semi-annual).

**Date rolling**Date rolling comes into effect because many instruments can only pay out accrued interest onbusiness day s. This often results in interest accruing for a slightly shorter or longer period.Common date rolling conventions are:*"Following business day". The payment date is rolled to the next business day.

*"Modified following business day". The payment date is rolled to the next business day, unless doing so would cause the payment to be in the next calendar month, in which case the payment date is rolled to the previous business day. Many institutions have month-end accounting procedures that necessitate this.

*"Previous business day". The payment date is rolled to the previous business day.

*"Modified previous business day". The payment date is rolled to the previous business day, unless doing so would cause the payment to be in the previous calendar month, in which case the payment date is rolled to the next business day. Many institutions have month-end accounting procedures that necessitate this.**See also***

Day count convention **References****External links*** [

*http://www.isda.org/ ISDA*] - standards body governing day count convention alongside ISMA.

* [*http://www.isda.org/c_and_a/pdf/mktc1198.pdf ISDA*] - ISDA PDF discussion of ISDA/ISMA/AFB Actual/Actual day count conventions.

* [*http://jfin.org/ jFin*] pure java open source implementation of financial date arithmetic

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### Look at other dictionaries:

**accrued interest**— Interest earned between the most recent interest payment and the present date but not yet paid to the lender. Chicago Board of Trade glossary Interest that has been earned but not yet paid. For example, the interest earned by a bondholder between … Financial and business terms**accrued interest**— n. Interest due on the principal. The Essential Law Dictionary. Sphinx Publishing, An imprint of Sourcebooks, Inc. Amy Hackney Blackwell. 2008. accrued interest The interest being ea … Law dictionary**Accrued Interest**— 1. A term used to describe an accrual accounting method when interest that is either payable or receivable has been recognized, but not yet paid or received. Accrued interest occurs as a result of the difference in timing of cash flows and the… … Investment dictionary**Accrued interest**— The accumulated coupon interest earned but not yet paid to the seller of a bond by the buyer (unless the bond is in default). The New York Times Financial Glossary * * * accrued interest accrued interest ➔ interest * * * The interest accruing… … Financial and business terms**Accrued interest**— An ISO term. The interest that has been earned but not yet been paid. The number of days, when needed (for example in case of bonds), the currency code, and the amount of accrued interest to be added or to be deducted. [3n] 3a 15d. Interest… … International financial encyclopaedia**accrued interest**— noun : interest earned since last settlement date but not yet due or payable * * * interest accumulated at a given time but not yet due or paid. * * * accrued interest, interest that has accumulated at a given time but has not yet been paid … Useful english dictionary**accrued interest**— /əˌkru:d ɪntrəst/ noun interest which has been earned by an interest bearing investment ● Accrued interest is added quarterly … Dictionary of banking and finance**accrued interest**— interest accumulated at a given time but not yet due or paid. * * * … Universalium**accrued interest**— accumulated interest, interest which has built up over a period of time … English contemporary dictionary**accrued interest**— /əkrud ˈɪntrəst/ (say uhkroohd intruhst) noun the amount of interest accumulated at a given time but not yet paid (or received) … Australian English dictionary