NEW YORK ( TheStreet) -- After the housing and mortgage crisis of the past few years, you'd think people would have thought long and hard about how best to conduct their next home purchase or refinancing. But maybe not. A survey by Zillow ( Z), the home and mortgage-shopping site, finds that misconceptions abound, even as rising home prices and low mortgage rates draw people into the market in droves. Zillow found that "many homebuyers may be ill-prepared to take out a mortgage, answering basic questions about mortgage information wrong nearly one-third (32.5%) of the time." About a third of those polled did not know it's possible to get a mortgage with a down payment of less than 5%, and a quarter mistakenly believed they were obligated to get a loan from the lender that had given them a pre-approval. About a quarter also believed they'd get the lowest mortgage rate from the bank they do other business with, though shopping around can often unearth a better deal. One in five believe it's impossible for an underwater homeowner to get a mortgage, though 2.2 million of those homeowners have done so, Zillow says. Misunderstandings are not terribly surprising, since most people don't shop for a mortgage very often. But once one starts looking around, it's important to avoid mistakes that seem small but could be very costly in the long run. "All too often buyers focus on negotiating a lower home price and ignore the importance of finding the right loan," says Erin Lantz, Zillow's director of mortgages. "If a homebuyer can lower their interest rate by even half a percentage point, they can not only increase their purchasing power, but save thousands of dollars over the life of the loan." The survey found that about a third of prospective homebuyers did not know the meaning of the term "annual percentage rate," which refers to the true yearly cost of the mortgage with points and origination and underwriting fees included. It is higher than the loan rate alone, and serves better for apples-to-apples comparisons of one loan with others. About half of those polled did not understand how quickly loan rates can change -- several times a day. That misunderstanding increases the prospect of overlooking better deals. About three in 10 of those polled believed that after a foreclosure or short sale it is impossible to get another mortgage without waiting at least seven years. In fact, a loan might be approved after only two to four years, though the lender is likely to require a large down payment -- 20% in many cases. Buying a home is obviously a major financial decision, the single largest one many people make. It pays to commit time to studying the market, the loan options and competing offers. Those who feel discouraged by stories of tight lending standards should keep in mind that lenders don't make money if they don't lend. As home prices continue to rise, mortgage lending becomes less risky, because there's a better chance of selling a home for enough to pay off the mortgage. That means lenders are likely to get a little freer with their money. The applicant can also improve the chances of approval by not pushing for the biggest loan possible. The lower the monthly payment relative to your income, the better your chances of getting the mortgage. You can accomplish that by buying a cheaper home or making a larger down payment, or both.