The Federal Housing Administration (FHA) is an agency within the Department of Housing and Urban Development (HUD). Its main goal is to help provide housing opportunities for low- to moderate-income families. FHA has single-family and multi-family mortgage programs but does not generally provide mortgage funds. Instead, it insures home loans made by private lenders.
Meanwhile, the Veterans Administration (VA) guarantees home loans made available to veterans, reservists and military personnel, without any down payment. VA loans frequently offer lower interest rates than normally available with other kinds of loans, thereby making it easier for veterans to qualify for a home loan.
The maximum loan amount VA will insure varies by region. There is no restriction on the purchase price as long as the borrower has the cash to make up the difference between the loan amount and the purchase price.