wrote:
Investment made at 16 was 2000

Although that is not relevant to the question you asked because you
assumed that you (will) have $9378 by age 20 somehow, if you are going
into the 2nd summer of work now, you will need to invest an average of
$1728 after each of the remaining 3 summers in order to accumulate
$9378 in assets at an average growth of 10.7%. This is given by the
following formula:

=pmt(10.7%, 3, -2000*(1+10.7%), 9378, 1)