When you are offered a "rate lock" from a lender, it means that you are guaranteed to get a specific interest rate over a determined period for the application process. This means your interest rate can't go up during the application process.
Although there can be a choice of rate lock periods (from 15 to 60 days), the longer spans are generally more expensive. A lending institution will agree to hold an interest rate and points for a longer span of time, such as 60 days, but in exchange, the rate (and sometimes points) will be more than with a rate lock of fewer days.
In addition to choosing the shorter rate lock period, there are more ways you can get the lowest rate. A bigger down payment will get you a lower interest rate, because you will be starting out with more equity. You can pay points to improve your rate for the loan term, meaning you pay more up front. One strategy that is a good option for many people is to pay points to improve the rate over the life of the loan. You'll pay more initially, but you'll come out ahead in the end.
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