Buying a property with a "Gift of Equity" down payment.

[Nick Hawkins]

I am buying an investment property from a family member for the $125k that they owe on it. The house appraises for $160k so I'm getting a $30k gift of equity to use as a down payment. The lender is telling me that the sale price will be $125k and that is what they are going to pay off of the existing $125k loan and give me a mortgage for $95k. That is the sale price minus the $30k equity down payment but I am having trouble wrapping my head around it. Can someone help me understand the lender paying out $125k and giving me a mortgage for $95k?