# Day Count Conventions

Key words: conventions, calculation Basis, Act/360, Act/Act, Act/365, 30/360, 30/360E, accrued interest Time must be synchronized among different market participants. Without adequate system market participants may calculate accrued interest differently.

Day count convention allows to calculate accrued interest that financial instrument pays taking into account Days, Months and Years.
Participants use conventions to obtain the same financial results. Conventions define the number of days between two coupon payments.
Usually periodic payments are shorter than one year but interest rates are expressed on a per annum basis.
Knowing interest rate per annum it is easy to calculate accrued interest on a short period of time by applying day count convention.The following formula is:

Accrued Interest = Nominal * Interest Rate * Day count convention

Different conventions are developed to address the needs of specific markets, like money market, bond markets etc.
The numerator is the number of days in a month while denominator is the number of days in a year.
The list of most common convensions is shown in the table below.

Convention
Calculation
Act/360, Money market The exact number of days divided by 360 days in the year. This convention is widely used for CDs, FRN, US Treasuty bills, MBS etc.
Act/365 Fixed, ISDA The exact number of days divided by 365
Act/Act, ISDA Number of days in a leap and non-leap years are taken into account. The start day is included and the last day is excluded from the calculation. A leap year have Act/366 convention.
Act/Act, ISMA The denominator is calculated as the number of days in the coupon period multiplied by the number of coupon periods in the year. The numerator is the exact number of days.
Act/Act, AFB/FBF The exact number of days divided by 365 if there is no 29th of February. Otherwise the denominator is 366.
30/360, Bonds Assumes there are 30 days in a month and 360 days in a year. This is also known as the Babylonian standard.

If Day1=31 then Day1=30. If Day2=31 and Day1=30 or 31 then Day2=30.
The algorithm calculates Number of days as:
360*(Year2-Year1)+30*(Month2-Month1)+(Day2-Day1).
Theere is also a function in Excel DAYS360 to evaluate number od days in the preiod.

30E/360, Eurobonds This is a Eropean version of 30/360. The difference from the above convention is that:
If Day1=31 then Day1=30. If Day2=31 then Day2=30.
The formula is:
Number of days = 360/(Year2-Year1)+30*(Monthe2-Month1)+(Day2-Day1).
The function DAYS360 uses the third parameter TRUE in order to apply 30E/360 convention.

30/360 Example . Let’s assume we have eurobond with \$100 notional and 5% paid semi-annualy (or 10% p.a.). Taking into account the preiod that starts from 01 January 2013 to 01 June 2013, what is the interest that earned?
First of all, we calculate number of days in the period. Using DAYS360 formula in Excel, we find the number is 150. Interest is paid semi-annualy(180 days) so we have 5%*\$100*(150/180)=\$4.166.