When you are promised a "rate lock" from the lender, it means that you are guaranteed to keep a particular interest rate for a certain number of days for your application process. This ensures that your interest rate won't rise during the application process.
Rate lock periods can vary in length, anywhere from fifteen to sixty days, with the longer spans generally costing more. The lender can agree to hold an interest rate and points for a longer span of time, say 60 days, but in exchange, the rate (and sometimes points) will be higher than with a rate lock of fewer days.
In addition to going with the shorter lock period, there are several ways you are able to attain the lowest rate. The more the down payment, the smaller your interest rate will be, because you will be starting with more equity. You may choose to pay points to bring down your rate for the life of the loan, meaning you pay more initially. One strategy that is a good option for many people is to pay points to bring the rate down over the life of the loan. You will pay more initially, but you will come out ahead, especially if you don't refinance early.
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