I think you are correct. You would expect that after 2000 years the proportion of C14 remaining compared to its original concentartion would be 77.9%. So since the shell has only 0.83%, it must be much older than 2000 years. You can determine just how old it is using:

, so:

years.

The only other thing I can think of is that perhaps there is a typo in the problem statement. If the ratio of C14 was 0.833 instead of 0.833%, it would lead to an age of about 1462 years. Seems to me that's a more "reasonable" result than 38,300 years.