Loan Officer that the leaves of mortgage rates and credit score?

Hello, I was shopping for a mortgage and I came across a loan officer who sends me to list the rates daily and open for 0.625 points credit costs. For example, his list yesterday, the rate set at 30 years was set at 4.875 0,125 points, he said that my rate will be 4.875, and it gives me a credit of 0.5 points on the loan amount. Can we really believe that this rate sheet and it is a good deal? Thank you in advance for your help.

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