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The total cost of the tuition is $8,880 and his parents are contributing $6,000 for his first year, so he needs to save $8,880 - $6,000 = $<<8880-6000=2880>>2,880.
He has 2 years to save, so he needs to save $2,880 / 2 = $<<2880/2=1440>>1,440 each year.
He needs to save $1,440 / 12 = $<<1440/12=120>>120 each month. Answer: \boxed{120}.