I'm with you on this one.
Left side of equation = what you keep in 2nd periode, should be bigger than the consumption in the second period:
More essential than me (only a Masterstudent of economics) agreeing with you is the fact that the result in (1) is the intertemporal budget constraint given in my coursnotes on Diamond's model of overlapping generations which utility function wise is exactly the same model you are using...
So I guess your professor is wrong, which can be very annoying when they don't want to admit it...
btw F.O.C. give then that
Studying for an exam on macro or growth economics?
good luck, mine is due in 2 days !