Maybe a Mortgage Broker can chime in on this; but I'll go way out on a limb and say that "Conventional" always involves a 80/20 Loan to Equity relationship. Conventional requires a 20% Downpayment.
Any Loan requiring less than a 20% D.P. has some kind of PMI built in to cover the Lender's exposure for the missing 20% D.P. That may take the form of FHA or VA, MGIC, GE Credit, or a whole host of State specific programs. Some Insurer has to become involved in protecting the Lender from any loss exceeding 80%, and the Buyer will pay a Premium for this Insurance. With VA and FHA, it is the U.S. Tax Payer who pays the bulk, or all, of the PMI Premium.
In your case, the Buyer is going to be paying a PMI Premium to someone. The Premium may be a one time cost at Closing, or it may be monthly for the length of time his equity is less than 20% (say the 1st 10 years of a 30 Mortgage) That may not have been disclosed to him yet; but I think it's there, in the cards, lurking. They should plan for this additional cost.
I doubt that these folks have actually been to a Lending Institution yet, and haven't been Pre-Qualified OR Pre-Approved. And I'd worry about making them a "Client", if they are fabricating their story at this stage. Good Luck.
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Dale C. Hittle of GOLDEN RULE PROPERTIES in Glover, Vermont
Where We're Always Striving To Put Together "THE FAIR DEAL"