The firefighter earns $30/hour * 48 hours/week = $<<30*48=1440>>1440 in a week.
In a month, the firefighter earns $1440/week * 4 weeks/month = $5760
His total monthly payment is 1/3 * $5760 = $<<1/3*5760=1920>>1920
His total monthly expenses are $1920 for rent + $500 for food + $1000 for taxes = $<<1920+500+1000=3420>>3420
The total amount of money the firefighter has after his expenses is $5760 - $3420 = $<<5760-3420=2340>>2340
#### 2340