int tuition, projectedTuition;
tuition = 6000;
for(int n=1; n<=5; n++) //Process
projectedTuition = tuition * 1.02;
cout << projectedTuition << '\n';
//THIS IS WHAT WAS MISSING!!!
tuition = projectedTuition;
Check out line 17. That's resetting the tuition variable to the amount that has the 2% increase. That way, next time through the loop, you'll have an updated value for tuition.
You can accomplish this in less space, with fewer variables, but this is an explicit demonstration of why your code isn't behaving the way you probably want it to.