Act/360, and why the day count matters

Dividing an annual rate by 360 instead of 365 makes the real rate slightly higher than quoted.

To charge daily interest, a lender must convert an annual rate into a daily one. That requires choosing what a year is. The choice is called the day-count convention, and it is a real term of the loan even though it never appears in the headline rate.

Act/360 means: count the actual days elapsed, but divide the annual rate by 360. That combination is not symmetrical. You are charged for all 365 days that actually happen, at a daily rate computed as though a year had only 360. The result is that the effective annual rate is the quoted rate times 365 over 360, which is about 1.39 percent higher in relative terms.

So a quoted 6.50 percent on an Act/360 basis costs the same as 6.59 percent on an Act/365 basis. On $500,000 that difference is about $451 a year. Not enormous, and also not zero, and entirely invisible in the rate you were quoted. Act/365 divides by 365 and has no such gap. Some conventions, such as 30/360, also adjust the day count itself.

The convention is not a trick — it is a long-standing money-market standard. But it is a term, and comparing two quoted rates on different conventions compares two different things.

The other place the convention bites is verification. If you rebuild a month's interest using 365 as the divisor and the lender used 360, your figure will be low by about 1.4 percent and you will conclude you have found an error where none exists. Matching the convention is the first step in checking any interest leg.

Key terms

Day-count convention: The rule for converting an annual rate into a daily one and counting days. Common forms are Act/360, Act/365 and 30/360.
Act/360: Charge for every day that actually elapses, using an annual rate divided by 360. Slightly more expensive than the quoted rate implies.
Effective annual rate: What you actually pay over a year once the convention and any compounding are applied.

Worked example

The 1.39 percent nobody quotes

$500,000 borrowed for one full year at a quoted 6.50%.

Act/365 daily rate: 0.0178082%
Act/365 annual interest: $32,500.00
Act/360 daily rate: 0.0180556%
Act/360 annual interest: $32,951.39
Difference: $451.39

Two loans quoted at the same 6.50% differ by $451 a year because of a divisor that appears in the fine print and not in the offer.

Check yourself

You rebuild a 31-day interest charge on $300,000 at 6.00% using 365 as the divisor and get $1,528.77, but the statement says $1,550.00. What is the likely explanation?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.