Premiums for employer-provided health insurance increased by relatively modest amounts for the second year in a row, according to a new survey, further evidence that once-fierce health care inflation might be abating.

The average annual premium for a family is now $16,351, up 4 percent from last year, according to the results of the survey released on Tuesday by the Kaiser Family Foundation. Of that amount, workers paid an average of $4,565. Premiums for individual policies purchased through an employer rose nearly 5 percent, to $5,884 annually, from $5,615 in 2012. The average contribution from the worker is $999.  Read more