Very confusing: 1) when to use continuous compounding. 2) So when are we going to use 360 days and when to use 365 days?

Use continuous compounding has a couple uses that come to mind. Number one, it values can be algebraically manipulated with other numbers easier if you use continuous compounding. For instance, if you use continuous compounding for both convenience yield and storage cost you can add/subtract them. It doesnâ€™t work without. Also it is a better representation for things that pay frequently, such as a stock index. Although daily compounding would work, contiuous allows for the algebraic manipulations. Basically I remember that any question that has LIBOR in it has a rate based on 360 day year