Interest calculations using Time Counting Methods
What is a Time Counting Method?
Time Counting Method in Q2 Loan Servicing is a day counting method used to determine the number of days in a year and the number of days in a month to be considered for the calculation of interest for a given period of time. It helps to provide standardized methods for calculating interest accruals on various loan products. It determines how interest is accrued over a period of time for a variety of investments, loans, or mortgages.
For example, if the Time Counting Method selected is Month and Days, which considers that the number of days in a year are 360 and the number of days in a month are 30, then for a due date that falls on the first of every month, the interest accrued on every due date is calculated as follows:
= P x N x R
where:
P = Principal amount on which interest is to be calculated.
N = Number of days
R = Annual rate of interest
= P x Interest rate per day x N
where:
Interest rate per day = R/number of days in a year
= P x (R/number of days in a year) x N
= (P x R/360) x 30
Thus, the formula that the system uses to calculate interest is as follows:
Formula for calculating interest
Interest = {(Principal x Annual Rate of Interest) / Days in the Year } x Days in the Month
The number of days in a month and the number of days in a year in the preceding formula could vary for each FI.
The day-counting convention is a complication that stems at least in part from the shortcuts that were used in lending markets before the market participants had ready access to precise ways to determine interest.
Number of days in a year
The number of days in a year considered by an FI depends on various factors and determines how R and N is considered in the preceding formula. The number of days in a year that an FI considers can be any one of the following:
Always 365: Here, the number of days in a year is always considered to be 365.
365 for non-leap year and 366 for leap year: Here, the number of days in a year is based on whether or not it is a leap year.
Always 360: Here, the number of days in a year is always considered to be 360.
What are the different types of Time Counting Methods available in Q2 Loan Servicing?
Based on the preceding number of years considered in a year, Q2 Loan Servicing offers you the following five Time Counting Methods to select from to help calculate the interest accrual between two dates:
You can select any one of the preceding Time Counting Methods either while creating a lending product or a loan contract as highlighted in the following image:
Month and Days
When you select this method, the system considers that a year always has 360 days and hence every month has only 30 days. The interest per day is calculated as P x R/360.
While calculating the interest between two dates, the 31st of a month is ignored and February is considered to have 30 days. For example, if you have to calculate interest from January 30 to February 1, the system calculates interest for one day as all months are assumed to be of 30 days. Also, while calculating interest from February 28, 2023, to March 1, 2023, the system calculates interest for three days instead of one day.
While working on an Excel, to verify the calculations for Month and Days, you can use the following formula in excel:
DAYS360(start_date, end_date, [method])
For example, to calculate the number of days between February 28, 2024 and March 31, 2024, you can use the formula in Excel as follows:
This leads to the days counted as 32 as follows:
Actual Days (Actual/365)
When you select this method, the system considers that a year always has 365 days irrespective of a leap year, and hence, February will always be considered to have 28 days irrespective of the leap year. The interest per day is calculated as P x R/365.
For example, if you have to calculate interest from February 28 to March 1, the system counts one day and not two days even if it is a leap year.
366/365
When you select this method, the system considers that a year always has 365 days. Thus, the interest per day is calculated as P x R/365. However, even though the year is always considered to have 365 days, the month of February is considered to have 28 days in a non-leap year and 29 days in a leap year.
Actual Days (366)
When you select this method, the system considers that a year has 365 days in a non-leap year and 366 days in a leap year. Thus, P x R/365 is calculated as the interest per day for non-leap year and P x R/366 as the interest per day for a leap year.
Actual/360
When you select this method, the system considers that a year always has 360 days. The interest per day is calculated as P x R/360. However, the days in a month are considered to have the actual number of days based on whether or not the year is a leap year. Thus, the system considers 28 days in February in a non-leap year and 29 days in February in a leap year.
Daily accruals are calculated at the start of the next day (SOD) when the StartOfDayJob batch job runs in the morning. For example, the accrual for December 31 is calculated when the StartOfDayJob runs at the start of the day of January 1.
Thus, to calculate accrual from December 31 to January 5, the system considers the interest accrued on the SOD of January 1, January 2, January 3, January 4, and January 5.
Time Counting Methods explained in a snapshot
The following table describes each Time Counting Method in a snapshot:
| Time Counting Methods | Days in a month considered | Days in a year considered | Description |
|---|---|---|---|
| Month and Days (30/360) | 30 | 360 |
This method considers all months to be 30 days long and each year to be of 360 days.
Note:
For weekly and bi-weekly loans, the Time Counting Method is always Actual Number of Days/364 days. |
| Actual Days (Actual/365) | Actual days in a month, with the exception of February, which is always believed to have 28 days regardless of leap years. | 365 |
This method takes into account the actual amount of days in each month with February having 28 days regardless of whether the year is a leap year or not, and each year being 365 days long. So, regardless of leap years, the system counts 31 days for January, 28 days for February, and so on. |
| Actual Days (366) | Actual days in a month |
|
This method takes into account the actual days in a month, and considers a leap year to be 366 days long whereas a non-leap year to be 365 days long. This means that if the year is a leap year, then the system will count 29 days in February and 366 days in a year. |
| 366/365 | Actual days in a month | 365 |
This method takes into account the actual number of days in a month, but it assumes the year is 365 days long, regardless of whether it is a leap year. This means that if the year is a leap year, then the system will count 29 days in February but 365 days in a year. |
| Actual/360 | Actual days in a month | 360 |
|
In instances where the CL Loan Contract uses Financial Calculator Version 2.0, the system ignores February 29 and considers only 365 days as the actual number of days in a year.
For example, let us say there is a loan of the amount of $100,000 and an interest rate of 10%. The Time Counting Method selected is Month and Days, which means that the days in a month are considered as 30 and the days in a year are considered as 360. Then the interest accrued in a month is calculated as follows:
Interest = 100,000 x (10/100) x (30/360) = $833.33.
Examples
Example 1: Time Counting Method = Month and Days; Interest accrued on every due date
Let us say that the interest is to be calculated on every due date considering 360 days in a year (Month and Days), then the system counts the number of days for which the interest is to be calculated as follows:
| Due Dates | Number of days in a month | Number of days for which the interest is to be calculated |
|---|---|---|
| January 31 | 30 days in January |
|
| February 28 | 30 days in February |
28 days From January 31 to February 28, the system counts 28 days. This is because the system considers 30 days for both January and February. |
| March 31 | 30 days in March |
32 days From February 28 to March 31, the system counts 32 days. This is because the system considers 30 days in each month including February and March. |
| April 30 | 30 days in April |
30 days From March 31 to April 30, the system counts 30 days. This is because the system considers 30 days for both March and April. |
| May 31 | 30 days in May |
30 days From April 30 to May 31, the system counts 30 days. This is because the system considers 30 days for both April and May. |
While working on an Excel, to verify the calculations for Month and Days, you can use the following formula in excel:
DAYS360(start_date, end_date, [method])
For example, to calculate the number of days between February 28, 2024 and March 31, 2024, you can use the formula in Excel as follows:
This leads to the days counted as 32 as follows:
Example 2: Interest accrued between two defined dates for each Time Counting Method
Assume a loan with an interest rate of 8% and payment due dates of February 25, 2016, and then March 05, 2016. Then, the system calculates the interest accrued between these due dates as described in the following table:
2016 is a leap year.
Time Counting Method |
Per day interest | Number of days | Interest accrued for the period |
|---|---|---|---|
| Month and Days (30/360) |
P x (8/100) x (1/360) = (0.08/360) x P |
10 (25th to 30th Feb + 30th Feb to 5th Mar) |
Per day interest x Number of days = (0.08/360) x P x 10 |
| Actual Days (Actual/365) | (0.08/365)x P |
8 (25th to 28th Feb + 28th Feb to 5th Mar) |
(0.08/365) x P x 8 |
| Actual Days (366) | (0.08/366) x P |
9 (25th to 29th Feb + 29th Feb to 5th Mar)
Note:
Since 2016 is a leap year, the days in February are 29. |
(0.08/366) x P x 9 |
| 366/365 | (0.08/365)x P |
9 (25th to 29th Feb + 29th Feb to 5th Mar)
Note:
Since 2016 is a leap year, the days in February are 29. |
(0.08/365)x P x 9 |
| Actual/360 | (0.08/360)x P |
9 (25th to 29th Feb + 29th Feb to 5th Mar)
Note:
Since 2016 is a leap year, the days in February are 29. |
(0.08/360)x P x 9 |
Example 3: Interest accrued for different periods for each Time Counting Method
Assume a loan with an annual interest rate of 8%. Now let us look at how the interest is calculated for various periods using each of the following Time Counting Methods:
Example with Month and Days (30/360)
| Year | Period of calculation | Number of days | Number of days in a year | Per day interest | Interest accrued for the period |
|---|---|---|---|---|---|
| Leap year or Non-leap year | April 1 to May 1 | 30 | 360 | P x 1 x (8/100)/360 | P x (8/100)/360 x 30 |
| Leap year or Non-leap year | July 1 to August 1 | 30 | 360 | P x 1 x (8/100)/360 | P x (8/100)/360 x 30 |
| Leap year or Non-leap year | February 1 to March 1 | 30 | 360 | P x 1 x (8/100)/360 | P x (8/100)/360 x 30 |
| From leap year to non-leap year | December 1, 2016, to January 1, 2017 | 30 |
360 | P x 1 x (8/100)/360 | P x (8/100)/360 x 30 |
| From non-leap year to leap year | December 1, 2015, to January 1, 2016 | 30 | 360 | P x 1 x (8/100)/360 | P x (8/100)/360 x 30 |
Example with Actual Days (Actual/365)
| Year | Period of calculation | Number of days | Number of days in a year | Interest |
|---|---|---|---|---|
| Leap year or Non-leap year | April 1 to May 1 | 30 | 365 | P x (8/100) x (30/365) |
| Leap year or Non-leap year | July 1 to August 1 | 31 | 365 | P x (8/100) x (31/365) |
| Leap year or Non-leap year | February 1 to March 1 | 28 | 365 | P x (8/100) x (28/365) |
| From leap year to non-leap year | December 1, 2016, to January 1, 2017 | 31 |
365 | P x (8/100) x (31/365) |
| From non-leap year to leap year | December 1, 2015, to January 1, 2016 | 31 | 365 | P x (8/100) x (31/365) |
Example with Actual Days (366)
| Year | Period of calculation | Number of days | Number of days in a year | Per day interest |
|---|---|---|---|---|
| Leap year | April 1 to May 1 | 30 | 366 | P x (8/100) x (30/366) |
| Non-leap year | April 1 to May 1 | 30 | 365 | P x (8/100) x (30/365) |
| Leap year | July 1 to August 1 | 31 | 366 | P x (8/100) x (31/366) |
| Non-leap year | July 1 to August 1 | 31 | 365 | P x (8/100) x (31/365) |
| Leap year | February 1 to March 1 | 29 | 366 | P x (8/100) x (29/366) |
| Non-leap year | February 1 to March 1 | 28 | 365 | P x (8/100) x (28/365) |
| From leap year to non-leap year | December 25, 2016, to January 25, 2017 |
December 25 to January 1 in leap year + January 1 to January 25 in non-leap year = 7 days in leap year + 24 days in non-leap year |
366 for leap year and 365 for non-leap year |
P x (8/100) x (7/366) + P x (8/100) x (24/365) |
| From non-leap year to leap year | December 25, 2023, to January 25, 2024 |
December 25 to January 1 in non-leap year + January 1 to January 25 in leap year = 7 days in non-leap year + 24 days in leap year |
365 for non-leap year and 366 for leap year |
P x (8/100) x (7/365) + P x (8/100) x (24/366) |
While using Actual Days (366), when interest is to be calculated for a period that crosses the year from non-leap year to leap year or vice versa, such as from December 25, 2023, to January 25, 2024, the system calculates the interest as the sum of the following:
-
Interest between December 25, 2023, to January 1, 2024, for 7 days, considering 365 days in a year
Here, the interest calculated on January 1 SOD (Start of Day) is for the previous year and hence the interest calculated on January 1 must consider 365 days in a year and not 366 days in a year.
Interest between January 1, 2024, to January 25, 2024, for 24 days, considering 366 days in a year.
Thus, although the accrual process is still run during SOD (January 1 morning), the system takes the number of days in a year for calculation purposes from the previous year. This is because the actual amount that is calculated on January 1 of any year belongs to the previous years accounting. Because of this, the system uses the previous years days in a year to calculate the interest.
This behavior is only applicable for Time Counting Method - Actual Days (366) from Platinum release onward. Before the Platinum release, the system calculated the January 1, 2024, accrual considering 366 days in a year.
Example with 366/365
| Year | Period of calculation | Number of days | Number of days in a year | Per day interest |
|---|---|---|---|---|
| Leap year | April 1 to May 1 | 30 | 365 | P x (8/100) x (30/365) |
| Non-leap year | April 1 to May 1 | 30 | 365 | P x (8/100) x (30/365) |
| Leap year | July 1 to August 1 | 31 | 365 | P x (8/100) x (31/365) |
| Non-leap year | July 1 to August 1 | 31 | 365 | P x (8/100) x (31/365) |
| Leap year | February 1 to March 1 | 29 | 365 | P x (8/100) x (29/365) |
| Non-leap year | February 1 to March 1 | 28 | 365 | P x (8/100) x (28/365) |
| From leap year to non-leap year | December 1, 2016, to January 1, 2017 | 31 |
365 | P x (8/100) x (31/365) |
| From non-leap year to leap year | December 1, 2015, to January 1, 2016 | 31 | 365 | P x (8/100) x (31/365) |
Example with Actual/360
| Year | Period of calculation | Number of days | Number of days in a year | Per day interest |
|---|---|---|---|---|
| Leap year | April 1 to May 1 | 30 | 360 | P x (8/100) x (30/360) |
| Non-leap year | April 1 to May 1 | 30 | 360 | P x (8/100) x (30/360) |
| Leap year | July 1 to August 1 | 31 | 360 | P x (8/100) x (31/360) |
| Non-leap year | July 1 to August 1 | 31 | 360 | P x (8/100) x (31/360) |
| Leap year | February 1 to March 1 | 29 | 360 | P x (8/100) x (29/360) |
| Non-leap year | February 1 to March 1 | 28 | 360 | P x (8/100) x (28/360) |
| From leap year to non-leap year | December 1, 2016, to January 1, 2017 | 31 |
360 | P x (8/100) x (31/360) |
| From non-leap year to leap year | December 1, 2015, to January 1, 2016 | 31 | 360 | P x (8/100) x (31/360) |