Day Count Conventions

Quick Version

A Day Count Convention is essentially a method of counting days for financial calculations. It might sound complex, but it’s really just about counting days in different ways.

Choosing the right convention for your calculation can be confusing due to the various options available. However, most loan repayment calculations use a limited subset of conventions available in Curo Calculator, with others reserved for more specialised scenarios. If you’re looking for guidance on which to use, here are our recommendations:

• Solving unknown values and implicit interest rates:

  • For calculations with repayments in months or multiples of months, use 30/360. This convention is often considered the de facto standard for many financial calculations and has been in widespread use for decades.
  • For calculations with repayments in weeks or multiples of weeks, opt for Actual/365 or Actual/Actual. Avoid conventions based on a 30-day month as these might yield unexpected results due to how they handle periods spanning month ends.

• Solving unknown APRs and unknown values using an APR:

  • For users in the European Union (EU), use the built-in EU 2023/2225 APR convention.
  • For users in the United Kingdom (UK), select the UK Mortgage APR for credit agreements secured on land or UK Non-Mortgage APR for those not secured on land.
  • For users located elsewhere, choose conventions with the EAR (Effective Annual Rate) suffix, e.g., 30/360 EAR. These conventions often mirror legally defined APR methods, providing a good proxy. If your jurisdiction has a mandated APR convention, please let us know, and we’ll consider adding support in a future release.

Continue reading for a deeper understanding of Day Count Conventions in general.

Deep Dive Version

All conventions supported by Curo Calculator are listed below, each with details to help you select the most appropriate one for your needs.

Each standard convention has a counterpart EAR (Effective Annual Rate) convention, which isn’t described separately as they use the same method of counting days. They differ only in where they start the day count from; in standard conventions, the count is based on the duration between the current and previous cash flow. In the EAR version, the count is the duration between the current and the initial advance or drawdown. This method effectively annualises the interest rate.

One final point: No matter which convention you use, it’s very easy to inspect the day counts applied to each cash flow in a repayment schedule. This way, you can sense-check if your chosen convention is working as expected. For further information, see Core Concepts > Schedules.

Here are the supported conventions:

EU 2023/2225 APR

Description:

• This convention expresses time intervals in years, months, or weeks, considering the frequency of drawdowns and payments.

Mathematical Logic:

• When intervals can’t be expressed in whole periods, the remaining days are calculated backwards from the cash flow date to the initial drawdown, divided by 365 (or 366 in a leap year).

Use Cases:

• Mandatory for computing the Annual Percentage Rate of Charge (APRC) for Consumer Credit in the EU.

Historical Context:

• Implemented with the EU’s Consumer Credit Directive 2023/2225.

Example:

• Weekly: From January 1 to February 4 would be counted as 5 weeks (divided by 52 weeks in a year).
• Monthly: From January 1 to March 1 would be counted as 2 months (divided by 12 months in a year).

UK Mortgages APR (UK CONC App 1.1)

Description:

• This convention is used for calculating the Annual Percentage Rate of Charge (APRC) specifically for consumer credit agreements secured on land in the United Kingdom.

Mathematical Logic:

• Periods are measured in whole calendar months or weeks when possible. For periods that don’t align with whole months or weeks, time is converted into years and days.
• Whole months or weeks are converted to years; any remaining days are expressed as a fraction of a year based on the year’s actual number of days (365 or 366 for leap years).

Use Cases:

• Essential for mortgages and other credit agreements where the security is land in the UK.

Historical Context:

• Derived from the UK’s Financial Conduct Authority (FCA) Consumer Credit sourcebook (CONC), specifically Appendix 1.1.

Example:

• If a period spans from January 1 to April 1, it would be counted as 3 whole months (divided by 12 for the year fraction), or if from January 1 to January 29, it might be considered as 29 days (divided by 365 or 366 for a year fraction).

UK Non-Mortgages APR (UK CONC App 1.2)

Description:

• This convention applies to calculating the Annual Percentage Rate of Charge (APRC) for consumer credit agreements not secured on land in the United Kingdom.

Mathematical Logic:

• Time intervals between dates are calculated directly in years or fractions thereof.
• A year can be viewed as having 365 days (or 366 in leap years), 52 weeks, or 12 equal months.
• For irregular periods, the time is converted into a fraction of a year based on the number of days in the year (365 or 366 for leap years).

Use Cases:

• Applicable for various forms of consumer credit like loans, credit cards, etc., where no land is involved as security.

Historical Context:

• Also part of the UK’s FCA CONC sourcebook, with specifics in Appendix 1.2.

Example:

• From January 1 to January 31 would be 31 days, considered as a fraction of 365 (or 366 in a leap year) for the year. If from January 1 to March 1, it would be counted as 2 months (divided by 12 for the year fraction), or alternatively, as 59 days.

30/360 Convention

Description:

• Assumes each month has 30 days and each year has 360 days for simplified calculations.

Mathematical Logic:

• Days are calculated as if every month ends on the 30th, regardless of actual days.

Use Cases:

• Preferred for bonds, fixed income, and standard loan calculations for its simplicity.

Historical Context:

• Developed for manual calculations before widespread computer use.

Example:

• Interest from January 1 to March 1 counts as 60 days (2 months x 30 days).

Actual/Actual (ACT/ACT) Convention

Description:

• Uses the actual number of days between dates and accounts for leap years.

Mathematical Logic:

• Counts every actual day, dividing by the year’s actual number of days (365 or 366).

Use Cases:

• Essential for precise interest calculations in government bonds and long-term securities.

Historical Context:

• Chosen for markets requiring accuracy over long periods.

Example:

• From January 1, 2024, to January 1, 2025, would be 366 days if it’s a leap year.

Actual/365 (ACT/365) Convention

Description:

• Counts actual days but uses a fixed 365-day year, ignoring leap years.

Mathematical Logic:

• Interest is calculated over actual days but with a constant year length.

Use Cases:

• Used in money markets, commercial loans, where leap years are less critical.

Historical Context:

• Designed for consistent annual rate calculations in short-term finance.

Example:

• From January 1 to June 1 counts over 365 days, regardless of leap years.

Actual/360 (ACT/360) Convention

Description:

• Employs actual days but assumes each year has 360 days for calculations.

Mathematical Logic:

• Results in higher annualised rates due to the smaller denominator.

Use Cases:

• Common in U.S. banking for short-term debt where a higher annual rate is acceptable or required.

Historical Context:

• Adapted from European practices for U.S. markets.

Example:

• From January 1 to January 31 counts as 31 days over 360, leading to a higher annual percentage rate compared to 365 or 366 days.