When you are offered a "rate lock" from a lender, it means that you are guaranteed to get a particular interest rate for a determined period for your application process. This ensures that your interest rate won't get higher while you are working through the application process.
While there might be a choice of rate lock periods (from 15 to 60 days), the extended ones are usually more expensive. The lending institution can agree to freeze an interest rate and points for a longer period, such as 60 days, but in exchange, the rate (and sometimes points) will be higher than with a rate lock of a shorter period.
In addition to choosing the shorter rate lock period, there are other ways you may be able to score the lowest rate. The larger down payment you can make, the smaller your interest rate will be, as you will be entering the loan with more equity. You could choose to pay points to reduce your rate over the loan term, meaning you pay more up front. One strategy that is a good option for many people is to pay points to bring the rate down over the term of the loan. You are paying more initially, but you will come out ahead, especially if you don't refinance early.
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