Dead battery

[salnj]

The week before last I bought a 1 owner 67k e53 3.0 L sports Package. Today I went in the morning to move it outside temperature was 35 degrees the car was cold dead. The car will not start. I tried to jump start the car and the result was the same. So I put it on the charger and the battery showed that it was totally discharged. Charged the battery and let the wife drive it for the day. Took it out tonight and all is good. I checked the voltage in the dash with the car running, light on and I got a reading of 12.9-13.00 V Drove the vehicle and the voltage was up to 13.2-13.3 V.

Do in need to worry about anything or is this the normal expected reading.