Exista functie built-in pentru calcul diferenta date (NSDateComponents fromDate toDate):
NSDate *now = [NSDate date];
NSDate * then = [NSDate dateWithTimeInterval:-172800 sinceDate:now];
NSDateComponents *compo = [[NSCalendar currentCalendar] components:NSDayCalendarUnit
fromDate:now
toDate:then
options:0];
NSInteger days = [compo day];
NSLog(@"Days diff: %d", days);