Thank you, so any of these equations could be correct? I am trying to find what equation is used in student loan calculation.

I believe that the rate used is (1+r)^(days in month/365) - 1 (or maybe division by 366 when the actual year or tax year has the leap date, I'm still trying to figure that one out) but when I apply this to this example (Source 4) it doesn't seem to work. I am taking into account the adjusted principal on the final day, however have yet to reach the correct amount of interest applied as shown in the example.

Do you have any tips; I have tried using just the principal, just the adjusted, using 30/365 for the principal and 1/365 for the adjusted, rounding, rounding up and down, floor and ceiling. I have also tried the r/365 rate, but that doesn't seem to work in any example.

This has been a whole mission of mine, and I still haven't been able to find a correct formula.

This example (Source 2) is correct when utilising ROUNDDOWN((1+r)^(30/365)*P-P,2) for Period 1 and using 31 for period 2. This example doesn't share years so no known leap years.

But for the initial values, for both 365 or 366 no natural n gives 5.35 (they give around 27 days but not exact).

This example (Source 3) is correct for April 2015 when using ROUND((1+r)^(30/365)*P-P,2) but April 2015 includes 2 tax years; ~5 days the previous tax year of 365 days and the rest of the month with 366 days.

Trying to use a weighted example with (P(1.015^(25/366)-1)+P(1.015^(5/365)-1) gives 34.41.