The bottom line is that it depends on the lender. A traditional lender (Wells Fargo, B of A, Chase, etc) will take 24 to 48 hours to give a buyer a prequalification letter letting them know what they can afford. If they are good, they will start collecting what they need so when they enter a contract to purchase a home, they can meet the 17 day contingency period for loan approval. If they are average, there will be a mad scramble to meet the 17 days and will often require an extension, which sellers do not like.
The biggest trend in lending in our market is direct lending, of which we are fans. Direct lenders (Amerifirst, Guaranteed Rate, etc) will typically take 3 - 5 days and give a buyer a preapproval letter, which means they are approved for the loan and the rest is mechanics. As both listing and selling agents, we appreciate direct lenders because they are set up differently. Most every direct lender has the loan officers, loan processing and funding under the same roof. It allows for faster resolution of issues and streamlines the loan process. We had a direct lender close on an $895,000 purchase of one of our listings in 16 days. And one of the married couple was self employed. Our average closing rate with a direct lender is 24 days, where most of the traditional lenders are 30 to 45 days.