If you walk into a bank you don't currently do business with and deposit $20,000 and they give you $75,000, please let me know about it.
Other than that, if you have other collateral to pony up, then they'll talk to you. If the business you are buying has significant assets that the bank, if necessary, could take and sell to settle the debt (we're talking about land, building, inventory, furniture, fixtures, equipment, etc.) then they'll gladly give you maybe 70% of value. Most all lenders will require you to have some equity in the deal, so don't expect them to loan you 100% of what you need to buy the business. Some may require you to pledge your personal assets (home, car, life insurance, etc) as well.
Your existing bank may be more willing to work with you, on the facts that they have a history of what you are all about.
Also, ask the seller if they are willing to finance the sale.
And they might, depending on the assets being acquired. It doesn't hurt to ask. What you need to do is pull a loan package together. These are a set od documents that let the loan officer and loan committee know about you (personal bio, personal financial statements, etc), about the business (historical financials, your business plan, prospective financial statements, etc), and what ever other documents the lender wants to see. The neater and completness of the loan package, the better the chances are of securing the loan.
Talk to the bank about what they want to see, and start gathering it up. If you need help, contact a local CPA (and ask the bank for a recommendation or two) for assistance with the loan package.
The SBA website has a ton of information on loan packages.
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