Day Count Convention | Practical Law

Day Count Convention | Practical Law

Day Count Convention

Day Count Convention

Practical Law Glossary Item w-026-0314 (Approx. 4 pages)

Glossary

Day Count Convention

Also referred to as day count fraction (and sometimes, simply, day count). A factor used to determine how interest accrues under financial contracts, investments, and instruments, including:
  • Loans.
  • Notes.
  • Bonds.
  • Swaps.
Because months and years have different numbers of days, calculating interest for different periods can be complicated, confusing, and susceptible to error. To address this, day count conventions were developed to standardize this methodology, to avoid disputes and provide uniformity and transparency.
To calculate interest for a particular payment period, the following formula is used:
Interest amount = Principal amount/Notional amount x Interest rate x Day count fraction
Where:
  • The interest amount and principal/notional amount are each expressed as an amount of currency, often US dollars or euros.
  • The interest rate, whether fixed or floating, is expressed as a percentage per annum (for example, 6.00%).
  • The day count fraction is a fraction in which the numerator and denominator are determined by the day count convention specified by the parties in their financial contract.
Different markets, such as interest rate swaps, bonds, and money markets, and different financial transactions, such as credit agreements and mortgage loans, tend to use particular day count conventions, often with further refinements unique to transactions in different currencies and different geographic regions. The most commonly used day count conventions are:
  • 30/360. This convention deems all months to be 30 days in length and each year to be 360 days. Interest accrues at a daily interest rate equal to 1/360th of the interest rate, but for each full month is deemed to accrue for 30 days, regardless whether the month has 28, 29, 30, or 31 days.
  • 30/365. This convention deems all months to be 30 days in length and each year to be 365 days. Interest accrues at a daily interest rate equal to 1/365th of the interest rate, but for each full month is deemed to accrue for 30 days, regardless whether the month has 28, 29, 30, or 31 days.
  • Actual/360. This convention counts the actual number of days in each month but deems each year to be 360 days. Interest accrues at a daily interest rate equal to 1/360th of the interest rate. For any interest period, the amount of interest is determined by multiplying the daily interest rate by the actual number of days that have elapsed (and multiplying the resulting percentage by the principal or notional amount, as applicable).
  • Actual/365. This convention counts the actual number of days in each month but deems each year to be 365 days. Interest accrues at a daily interest rate equal to 1/365th of the interest rate. For any interest period, the amount of interest is determined by multiplying the daily interest rate by the actual number of days that have elapsed (and multiplying the resulting percentage by the principal or notional amount, as applicable).
  • Actual/actual. This convention counts the actual number of days in each month and the actual number of days in each year. Interest accrues at a daily interest rate calculated by dividing the interest rate by the actual number of days in the current year. For any interest period, the amount of interest is determined by multiplying the daily interest rate by the actual number of days that have elapsed (and multiplying the resulting percentage by the principal or notional amount, as applicable).
Example: A financial instrument with:
  • A principal or notional amount of $25 million.
  • A fixed interest rate of 3.00% per annum (yielding an annual interest amount of $750,000 ($25 million x 3.00%)).
  • Interest payable bi-monthly on the last day of every second month, with interest accruing from the day after payment to and including the following payment date.
This financial instrument produces different incremental interest amounts depending on the day count convention and timing of the payment.
If, for example, payment is due on the last day of February for the interest period beginning on January 1, under the:
  • 30/360 day count convention, the day count fraction is (30+30)/360 = 1/6. $750,000 x 1/6 = $125,000 interest amount.
  • 30/365 day count convention, the day count fraction is (30+30)/365 = 60/365. $750,000 x 60/365 = $123,287.67 interest amount.
  • Actual/360 day count convention, the day count fraction is (31+28)/360 = 59/360. $750,000 x 59/360 = $122,916.67 interest amount.
  • Actual/365 day count convention, the day count fraction is (31+28)/365 = 59/365. $750,000 x 59/365 = $121,232.88 interest amount.
  • Actual/actual day count convention, and if this was also a leap year, the day count fraction is (31+29)/366 = 60/366. $750,000 x 60/366 = $122,950.82 interest amount.