35 years=35*4=140 quarters.
If 6% is annual rate, quarterly rate=6/4=1.5%.
If $60 is deposited at the end of a quarter, it is not subject to interest for another quarter.
The first deposit of $60 has the benefit of 139 quarters' interest. The second deposit has 138 quarters' interest, etc. We can write a geometric series: 60*1.015^139+60*1.015^138+...+60*1.015+60.
This can be written 60(1+1.015+1.015^2+...+1.015^138+1.015^139).
The series sums to 60(1.015^140-1)/(1.015-1)=60*469.32=$28,159.25 approx. This is the amount after 35 years.