How a year is counted for interest — 30/360, ACT/360, ACT/365 — and they disagree.
A day count convention decides how the time between two dates is measured for accruing interest. ACT/365 counts actual days over a 365-day year; ACT/360 counts actual days over a 360-day one; 30/360 pretends every month has thirty days and every year three hundred and sixty.
These give different answers for the same period, and the differences are not rounding. ACT/360 accrues more interest than ACT/365 over the same days, because the denominator is smaller — which is why the choice is negotiated rather than assumed.
The 30/360 family exists from before computers, when a uniform month made manual calculation tractable. It survives because instruments written under it are still outstanding.
Business day convention picks the date. Day count measures the interval between dates. Similar names, unrelated jobs.
See also business day convention · roll convention · maturity date
We hold this as not held — a contract term, not a calendar fact. See what we hold.