According to a new report by Reis Inc., the average rent for a Boston apartment has jumped to over $2,000 a month. The finding follows a 1.3 percent rise in rents during the fourth quarter of last year, bringing the average rent to $2,010, or 5.5 percent more expensive than a year ago. The city’s vacancy rate rose 1.1 percent over the past year to 5.6 percent, almost a full percentage point higher than the 4.4 percent national average vacancy rate. The city saw 6,400 new apartment units hit the market in 2015, up from around 4,400 in 2014 and 2,400 units in 2013. Boston now has the fourth highest rental average among the 79 metro markets analyzed by Reis, lagging behind only only New York ($3,436), San Francisco ($2,491) and San Jose ($2,023).