Accrued interest
Encyclopedia
In finance
, accrued Interest is the interest
that has accumulated since the principal investment
, or since the previous interest payment if there has been one already. For a financial instrument such as a bond
, interest is calculated and paid in set intervals. Accrued income is an income which has been accumulated or accrued irrespective to actual Receipt, which means event occurred but cash not yet received.
where
is the accrued interest, 
is the fraction of the year, 
is the principal, and 
is the annualized interest rate.
is calculated as follows:
where
is the number of days in the period, and 
is the number of days in the year.
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.
A compounding instrument adds the previously accrued interest to the principal each period, applying compound interest
.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, accrued Interest is the interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....
that has accumulated since the principal investment
Investment
Investment has different meanings in finance and economics. Finance investment is putting money into something with the expectation of gain, that upon thorough analysis, has a high degree of security for the principal amount, as well as security of return, within an expected period of time...
, or since the previous interest payment if there has been one already. For a financial instrument such as a bond
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
, interest is calculated and paid in set intervals. Accrued income is an income which has been accumulated or accrued irrespective to actual Receipt, which means event occurred but cash not yet received.
Formula
The primary formula for calculating the interest accrued in a given period is:where
is the accrued interest, is the fraction of the year, is the principal, and is the annualized interest rate. is calculated as follows:where
is the number of days in the period, and is the number of days in the year.The main variables that affect the calculation are the period between interest payments and the day count convention
Day count convention
In finance, a day count convention determines how interest accrues over time for a variety of investments, including bonds, notes, loans, mortgages, medium-term notes, swaps, and forward rate agreements . This determines the amount transferred on interest payment dates, and also the calculation of...
used to determine the fraction of year, and the date rolling
Date rolling
In finance, date rolling occurs when a payment day or date used to calculate accrued interest falls on a holiday, according to a given business calendar. In this case the date is moved forward or backward in time such that it falls in a business day, according with the same business calendar.The...
convention in use.
A compounding instrument adds the previously accrued interest to the principal each period, applying compound interest
Compound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...
.