In a former life, I helped banks install loan servicing software. In every installation, there came a point where the bank would have to decide which accrual method to use for its loan portfolio. When we got to this point, the Loan Operations manager would always turn to me and say, “what’s the difference between 30/360, Actual/360, and Actual/365, and which one should we go with?”
Although minor, the differences between loan accrual methods can result in multi-thousand dollar variations in interest paid over the term of a loan. As such, it’s important to be aware of these accrual methods, their differences, and how each one is calculated. With this knowledge, hopefully you’ll be able to save a few dollars in interest the next time you obtain a loan. So here’s the agenda with this article:
- Example scenario
- 30/360 Accrual Method
- Actual/365 Accrual Method
- Actual/360 Accrual Method
- Side by Side comparison
In order to best demonstrate the differences between accrual methods, a loan example is needed: Here’s the scenario:
|# Payments Per Year:||12|
|Loan Term:||10 Years|
|Calculated Monthly Payment:||$25,311.28|
Although the loan payment is the same, the portion that goes to principal and the portion that goes to interest will vary with each of the 3 accrual methods. Let’s look at each method individually before comparing them side by side.
Method 1: 30/360
Calculating accrued interest using the 30/360 method is a straightforward process using the following steps:
- Calculate the Daily Accrual Rate: Identify the annual interest rate, 4.00%, and divide it by 360 to get the daily accrual rate. 4.00% / 360 = .011 %
- Calculate the Monthly Accrual Rate: Multiply the daily accrual rate by 30 to get the monthly accrual rate: .011% * 30 = .333%.
- Calculate the Monthly Accrued Interest: Multiply the monthly accrual rate by the outstanding balance to get the monthly interest accrual amount: $2,500,000 * .333% = $8,333.33
Using the 30/360 accrual method, $8,333,33 of the month one payment is applied to interest and the remaining $16,977.95 is applied to principal. Over the 10 year term of the loan, the borrower would pay a total of $537,354 in interest in addition to the $2,500,000 in principal repaid.
With the 30/360 method, the daily accrual amount is higher because the interest rate is divided by 360 days, not 365 (which is the actual number of days in a year). However, the total amount of interest is the lowest of the 3 methods because it only accrues for 30 days each month, even in months that have 31 days.
Method 2: Actual/365
The calculation method for Actual/365 is slightly different than 30/360 in that the interest rate is divided by 365 days, not 360. Using the same example, here’s how to calculate the monthly accrued interest:
- Calculate the Daily Accrual Rate: Identify the annual interest rate, 4.00%, and divide it by 365 to get the daily accrual rate: 4.00% / 365 = .011%
- Calculate the Monthly Accrual Rate: Multiply the daily accrual rate by the actual number of days in a given month. For example, January has 31 days so the monthly accrual rate for January is: .011% * 31 = .340%. February has 28 days so the monthly accrual rate is: .011% * 28 = .307%
- Calculate the Monthly Accrual Amount: Multiply the monthly accrual rate by the outstanding balance. For January, the monthly accrual amount would be: .340% * $2,500,000 = $8,493.15
Using the Actual/365 accrual method, $8,493.15 of the month one payment is applied to interest and the remaining $16,818.13 is applied to principal. Over the 10 year term of the loan, the borrower would pay a total of $537,396 in interest in addition to the $2,500,000 in principal repaid.
With the Actual/365 method, the daily accrual amount is slightly lower because the rate is divided by 365 days, not 360. However, the overall amount of interest is slightly higher because interest is accrued over a larger number of days (365 or 366 in a leap year).
NOTE: In this example, it is assumed that years 4 and 8 are leap years, which would accrue one extra day of interest.
Method 3: Actual/360
Of the 3 methods discussed, Actual/360 is going to result in the highest amount of interest paid over the term of the loan. Here’s how to calculate it:
- Calculate the Daily Accrual Rate: Identify the annual interest rate, 4.00%, and divide it by 360 to get the daily accrual rate: 4.00% / 360 = .011%
- Calculate the Monthly Accrual Rate: Multiply the daily accrual rate by the actual number of days in the month. For January, the monthly accrual rate would be: .011% * 31 = .344%
- Calculate the Monthly Accrual Amount: Multiply the monthly accrual rate by the outstanding balance. In month 1, the accrued interest would be: .344% * $2,500,000 = $8,611.11
Using the Actual/360 accrual method, $8,611.11 of the month 1 payment is applied to interest and the remaining $16,700.17 is applied to principal. Over the 10 year term of the loan, the borrower would pay a total of $547,154 in interest in addition to the $2,500,000 in principal repaid.
The Actual/360 accrual method results in the highest amount of interest paid over the term of the loan because it combines the “best” of the previous two methods. It has the highest daily accrual rate because the annual interest rate is divided by 360 and it has the highest monthly accrual amount because it is accrued over the actual number of days in the month.
NOTE: Because of the significant difference in interest paid under the Actual/360 accrual method, It’s worth noting that it has landed several banks in court. Ultimately, the banks prevailed because the interest calculation method was disclosed. However, make no mistake, banks are for-profit institutions and they have an incentive to use the Actual/360 method because it results in the most interest paid to them.
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Side by Side Comparison
Differences in the accrual methods are most easily demonstrated using a side by side comparison:
|30 / 360||Actual / 365||Actual / 360|
|Annual Interest Rate||4.00%||4.00%||4.00%|
|Daily Accrual Rate||.0111%||.0110%||.0111%|
|Monthly Accrual Rate||.3333%||.3397%||.3444%|
|Month 1 Interest(*1)||$8,333,33||$8,493.15||$8,611.11|
|Total Interest(*2)||$ 537,354.14||$ 537,396.13||$ 547,154.46|
*2 Assumes a $2,500,000 outstanding loan balance in month one
From the table, it’s clear that the difference between 30/360 and Actual/365 is minor, however, the difference between Actual/365 and Actual/360 is significant over the life of the loan. For this reason, it is important to be aware of the interest accrual methodology used in your next loan transaction. For the most part, 30/360 is used in consumer transactions (like mortgages) and Actual/365 and Actual/360 are used in commercial transactions.
Interest Accrual Model
To make things a bit easier for you, I’ve created a model that will calculate the interest accrued under each of the 3 methods and compare them side by side:
Here’s how to use it:
- Open the model
- Enter the loan amount, interest rate, and term in the cells highlighted in yellow
- Observe the summary differences in the table to the right. For a complete amortization schedule, click through the tabs at the bottom.
NOTE: The model can only handle loans up to 30 years in term.
In this article, we discussed three different loan accrual methods banks use to calculate interest on a commercial loan. The three methods are 30/360, Actual/365, and Actual/360. Each method results in a different amount of interest paid over the life of the loan. Understanding these methods could save you money next time you are borrowing money from a bank.