and what is the saying? 'He who measures, measures manure.' Nowadays, all battery chargers operate at 14.4V

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With a car that's 13 years old, your battery should still be in good condition after you turn off the engine (provided there are no electrical devices drawing power).
'You won't notice how powerful your battery is when you measure its resting voltage. What matters is the internal resistance of the battery when starting, or rather, what current it can still deliver. Consequently, the voltage drops.'