FHA 203k - a rehab loan
Jumbo for 'large' loans. "large" depends on the area.
USDA loans for rural area
There are many others.
They are often called "First Time Buyer" programs but they are not just for first time buyers. Also, "first time" doesn't really mean first time. These programs, offered by some government entities, some mortgage lenders, and sometimes organizations are almost always subject to income limits. While not restricted to low income individuals they are definitely not generally available for upper income buyers.
The Community Reinvestment Act (CRA) is a major first time buyer program offered by some lenders in designated areas. There are income limits but the rates are competitive and the loans do not require PMI - Private Mortgage Insurance.
Unless you are paying cash for your home your home you should ensure that your contract is contingent on you receiving the financing needed for the purchase.
All home buyers know that they will need to provide documentation to show that they qualify for a home purchase to their agent. They should also know
that the agent will have to provide that documentation to the seller at the time an offer is made. If they don't - the seller is unlikely to even consider the offer.
The seller's agent will help the seller evaluate the offer - and the documentation submitted to back it up. They will be more comfortable with documentation that comes from
a lender they (or at least your agent) are familiar with and that has experience with the type of loan involved in the area in which the purchase will take place.
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