The investor will short our funding of the loan for this Admin fee when it is sold to them.
That sounds like that is an administration fee being charged to the bank for the settlement of the loan into the secondary market and is not a fee associated with the borrower obtaining the loan. It's a fee for the bank selling the loan to this particular investor.
If the bank is passing that charge to the borrower then IMO that is part of the bank's origination fees for processing the loan and would be disclosed as such.
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The opinions expressed are mine and they are not to be taken as legal advice.