13th-month (not) bonus

I never really thought about it, but it was explained to me why we have this so-called 13th-month "bonus".
You see, we take 1 month to be 4 weeks, which works out to 48 weeks per year (4 weeks x 12 months). However, we know that 1 year has 52 weeks, which if you divide by 4, will give us 13 (months). Hence, actually, the 13th-month isn't really a "bonus", but what we should get for the "extra" month we worked.