Rents for apartments in Boston are soaring, and a dearth of new, cheaper apartments means many residents will have an increasingly difficult time finding an affordable place to live. The average monthly rent for a Boston apartment jumped more than 7 percent to $1,881 in the past year, according to RentalBeast.com , which follows the rental market in Boston neighborhoods. A two-bedroom apartment in the Back Bay now rents for $2,857 a month; in Jamaica Plain, $1,536.
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