Adjusting % for days of the year

Hey guys,

General question here, I’m trying to make memorising these formulas easier for myself, and i’m curious if anyone can explain to me why certain formulas use (1.05)^120/365 and others (1+(.05*(120/365)) for adjusting an interest rate based on the length of the loan. This is obviously assuming a 5% interest rate over 120 days.

I’m just trying to understand why certain formulas would use one over the other as they result in a very very similar number but certain formulas use one vs the other. Any help would be appreciated.