In June, Cory begins to save money for a video game and a TV he wants to buy in December. He starts with $20. Each month he plans to save 10% more than the previous month. How much money will he have at the end of December?
At the end of June, Cory saves 10/100*$20 = $<<10/100*20=2>>2 more than $20 he had at the start.
The total amount of money that he saves in June is $20+$2 = $<<20+2=22>>22
The total amount of money that he saves in July is 10/100*$22 = $2.2 more than what he had in June.
The total amount of money that he saves in July is $22+$2.2 = $<<22+2.2=24.2>>24.2
The total amount of money that he saves in August is 10/100*$24.2 = $2.42 more than what he had in July.
The total amount of money that he saves in August is $24.2+$2.42 = $<<24.2+2.42=26.62>>26.62
The total amount of money that he saves in september is 10/100*$26.62 = $2.662 more than what he had in august.
The total amount of money that he saves in september is $26.62+$2.662 = $<<26.62+2.662=29.282>>29.282
The total amount of money that he saves in October is 10/100*$29.282 = $2.9282 more than what he had in September.
The total amount of money that he saves in October is $29.282+$2.9282 = $<<29.282+2.9282=32.2102>>32.2102
The total amount of money that he saves in November is 10/100*$32.2102 = $3.22102 more than what he had in October.
The total amount of money that he saves in November is $32.2102+$3.22102 = $<<32.2102+3.22102=35.43122>>35.43122
The total amount of money that he will have at the end of December is $35.43122+35.43122*10/100 = $35.43122+$3.54312 = $<<35.43122+3.54312=38.97434>>38.97434. Answer: \boxed{38}.