# When computing with rates, how long is a year? how long is a day?

The convention says that when computing with rates, $1$ year has $360$ days. Does this mean that, when computing with rates, $1$ year has $360$ normal days or 1 day is $\frac{365 \times 24}{360} = 24.33$ hours long?

I hope it is clear, tell me if my question is confusing.

When the convention is ACT/360, it means that 365 calendar days of interest is calculated as 365/360 years. I knows it seems stupid, but before industrial use of computers, it was convenient for a year to be a nice round number like 360.

I forget how the 30/360 convention is handled - I once coded up all the conventions, but they have worked really well for me and I don't remember what they all mean!

Try this reference:

https://developers.opengamma.com/quantitative-research/Interest-Rate-Instruments-and-Market-Conventions.pdf

• Hours are never considered in interest payment calculations; the shortest period to borrow/lend money is 1 day. May 10 '17 at 23:45
• @noob2 - yes - closest thing I can think of that is an intraday loan is a tri-party repo arrangement, but I have never had to get down and dirty with that kind of nuanced business. May 10 '17 at 23:50
• What I wanted to know was that: Suppose that today is 01/01/2017 and I get a loan that I have to pay in 1 "year"; when do I need to pay the loan? If a "year" was 360 days long, each day of 24 hours, then I would have to pay it on 12/26/17. But if a "year" was 360 "days" long, each "day" of 24.33 hours, then I would have to pay it on 01/01/2017. May 10 '17 at 23:58
• Yeah, it is clear now. If I want to get a loan with a rate stated in "years" (of 360 days) and pay it in a year (of 365 days), then I need to pay amount * (1 + rate * 365/360), as stated by FGTCC. All that could be deduced if I was told that a "year" has 360 days of 24 hours. May 11 '17 at 0:14