For every $105 dollars Jim invested at the beginning of a certain year, he made $9.975. If, at the end of the year his investment was worth $876, how much, in dollars, had he put into this investment at the beginning of the year?
Jim made $9.975 for every $105 invested, so for every dollar he invested, he made $9.975/105 = $0.095.
If at the end of the year his investment was worth $876, then he had $876/$0.095 = $<<876/0.095=9210>>9210 invested at the beginning of the year. Answer: \boxed{9210}.