Assuming the battery isn't defective something must be drawing power from it when it is off.
The likely source will be the additions from the previous owner. Try disconnecting these and see if it helps. Generally things like stereos should have two power feeds, one from the battery (through a fuse box) and the other from the ignition (acc or accessory). The stereo draws its power from the battery and uses the acc signal to tell it when to turn off. Sometimes people install these incorrectly with the acc wire on the stereo or amplifier connected to the 12v line. Amplifiers also should have a signal line to the stereo to tell it when to turn off, this may also be missing?
Do you have a multimeter?