I will explain the problem with an example.
Today (14/03/2021) y agree a Zero-Coupon Mortgage with a nominal of a milion dolars an with an annual interest rate compounded annualy and with an ACT/360 basis of 3% and with a repayment at 31/07/2022.
As between the two dates there are 504 days what we will do is the following to compute the final payment value:
F.V. = P.V * (1 + r/m)^(m*t)
And as m = 1:
F.V. = P.V * (1 + r)^(t) = 1M * (1 + 0.03)^(504/360) = 1.042.250,5059
But the think is that, the interest is compounded only once (only compounded at 14/03/2022) and from that date until the end as no more interest is reinvested the interest earn untill maturity (for me) should be based on a normal interest rate so it should be divided intro first period 14/03/2021 until 14/03/2022 (annual compounding)+ period from 15/02/2022 to end (simple compounding) so:
F.V. = 1M * (1 + 0.03)^(365/360) * (1 + 0.03*(139/360)) = 1.042.358,67431
If it is not in this way how I have to threat this broken period as in this case the compounding for the second period will not occur until 14/03/2023.
Thank you in advance