Days In Year
The typical loan payment calculation doesn’t take into account non-uniform payment periods. In reality, not all months last 30 days and there are 52 weeks and one day in a year (two days for a leap year). This means that more interest will accrue in the month of January than in the month of February if interest is accruing daily. In LMS, you can calculate interest with the actual number of days in a year or month, or with uniform, level payments based on whatever frequency you're using.
Like you’d expect, this option calculates the interest that accrues daily and then multiplies it by the number of days in a payment period in order to get the total period interest accrual. This means interest accrues based on a 365-day year.
Interest Accrual Using Actual Days in Year
For instance, let's say we have a loan with a 25% interest rate. Dividing that by the number of days in a year (calculated as 0.25/365), we find that accrues 0.0685% interest each day. Then, we would multiply that 0.0685% by the number of days in a month. For a 31-day month, 0.0685% times 31 or 2.1232%. For a 30-day month (0.0685*30), we get 0.0205%. In February (0.0685*28), we get 1.9178%.
You could also calculate the amount of interest to accrue in any period by multiplying the annual interest rate by the ratio of days in the period to days in the year. Sticking with our 25% interest example, we could solve for a 31-day month with the equation 25*31/365, which gives us 2.1232%, the exact same as our earlier equation. The math is identical, so you can use whichever equation clicks best for you.
This option will calculate payments and accrue interest based on uniform payment periods for your payment frequency. That means that if you have a monthly frequency with a payment period of 30 days, and with 12 payment periods per year, the days in the year equal 30 (days in period) x 12 (payments per year) = 360. Semi-monthly payment periods also use a 360-day year because 15 x 24 = 360. Weekly and bi-weekly frequencies will use a 364 day year because 7 x 52 = 364 and 14 x 26 = 364.
When most people hear this, they ask the same question: where did the interest from those other days in the year go? Don't worry, you're still getting interest for those days. Rather than dividing the annual interest rate into 365 portions, the frequency method divides it into the number of payment periods (usually 12, 24, or 52).
Interest Accrual Using Frequency-Specific Days in Year
For a loan with 25% interest annual and monthly payments, we would divide 25% by 12 to get a period rate of 2.0833%. Then, to calculate the daily interest rate, we divide the period rate by the number of days in the month. For example, January would have a daily rate of 2.0833% divided by 31 days, or 0.0672% each day. February would have a daily rate of 2.0833% divided by 28, or 0.0744% each day.
The daily rates are different from month to month, but the monthly rates are the same, meaning the same total interest accrues in January, February, and every other month.
In this example, we will be looking at a 36-month loan for $12,000 at a 12% interest rate. If the Days in Year option is set to Frequency, the payment schedule is calculated to be 36 monthly payments of $398.69
If you change the setting to Actual, the payment schedule is calculated as 35 payments of $398.69 and 1 payment of $234.12.
You might be thinking, “I thought the Actual meant 4 extra days of interest, why does the borrower pay slightly less?” The explanation for this is in how the period interest rate is calculated. Here is how the first payment breaks down between interest and principal in a Frequency scenario:
As you can see, the interest portion of the first payment is $232.33. This is calculated as the monthly interest rate multiplied by the average daily balance for the payment period. To get the period interest rate, take the yearly rate of 25% and divide it by the number of payment periods in a year (12). This gives a monthly interest rate of 2.0833%. If we multiply that by the average daily balance for the first payment period of $11,152 we get 11,152 x .020833 (the percentage as a decimal) = 232.33, so $232.33 will be the interest portion of the first payment.
In an Actual scenario, the first payment breaks down as follows:
You can see that the interest portion for the first payment is $229.15. Since the payment periods in a monthly loan are actually of different lengths, we will calculate monthly interest as:
monthly interest = daily interest rate x average daily balance x number of days in the period
The daily interest rate is calculated as:
25% (yearly interest rate) / 365
When we plug in the numbers we get:
25% / 365 = 0.0684%
So 0.0684% is the daily interest rate. Since the average daily balance for the payment period is $10,000 and there are 30 days in the first payment period, interest for the period is calculated as:
.000684 (daily interest rate converted to a decimal) x 11,152 x 30 = 229.15
So, $229.15 worth of interest will accrue in this period.
You’ll notice if you multiply 0.0684% by 30 (days in the period) you get 2.0548% monthly interest. As we calculated above, the monthly interest rate for our Frequency scenario was 2.0833%. We could have calculated that rate in the same way as we calculated the rate in our Actual scenario as:
25% (yearly rate) / 360 (days in year) x 30 (days in period) = 2.0833%
Since our interest rate is slightly higher in the Frequency scenario, it compensates for the 4 days of “missing” interest. In most cases, the calculated payment schedules with either Days in Year selection will be quite close.