NSPredicate: filtering objects by day of NSDate property

Example on how to also set up startDate and endDate to the above given answer:

...

NSCalendar *calendar = [NSCalendar currentCalendar];
NSDateComponents *components = [calendar components:(NSCalendarUnitYear | NSCalendarUnitMonth ) fromDate:[NSDate date]];
//create a date with these components
NSDate *startDate = [calendar dateFromComponents:components];
[components setMonth:1];
[components setDay:0]; //reset the other components
[components setYear:0]; //reset the other components
NSDate *endDate = [calendar dateByAddingComponents:components toDate:startDate options:0];
predicate = [NSPredicate predicateWithFormat:@"((date >= %@) AND (date < %@)) || (date = nil)",startDate,endDate];

...

Here I was searching for all entries within one month. It's worth to mention, that this example also shows how to search 'nil' date-entires.

Given a NSDate * startDate and endDate and a NSManagedObjectContext * moc:

NSPredicate *predicate = [NSPredicate predicateWithFormat:@"(date >= %@) AND (date <= %@)", startDate, endDate];
NSFetchRequest *request = [[[NSFetchRequest alloc] init] autorelease];
[request setEntity:[NSEntityDescription entityForName:@"EntityName" inManagedObjectContext:moc]];
[request setPredicate:predicate];

NSError *error = nil;
NSArray *results = [moc executeFetchRequest:request error:&error];