Custom Core Data SectionNameKeyPath

The following should work: Implement the periodYear method (which will be used as "section name key path") in a class extension of your managed object subclass:

@interface Event (AdditionalMethods)
- (NSString *)periodYear;
@end

@implementation Event (AdditionalMethods)
- (NSString *)periodYear {
    return [self.acctPeriod substringToIndex:4];
}
@end

Make sure that acctPeriod is used as the first (or only) sort descriptor for the fetch request:

NSSortDescriptor *sortDescriptor = [[NSSortDescriptor alloc] initWithKey:@"acctPeriod" ascending:YES];
NSArray *sortDescriptors = @[sortDescriptor];
[fetchRequest setSortDescriptors:sortDescriptors];

Use periodYear as sectionNameKeyPath for the fetched results controller:

NSFetchedResultsController *_fetchedResultsController = [[NSFetchedResultsController alloc]
                  initWithFetchRequest:fetchRequest 
                   managedObjectContext:self.managedObjectContext 
                     sectionNameKeyPath:@"periodYear"
                              cacheName:nil];
_fetchedResultsController.delegate = self;
self.fetchedResultsController = _fetchedResultsController;

And finally add the default titleForHeaderInSection method:

- (NSString *)tableView:(UITableView *)tableView titleForHeaderInSection:(NSInteger)section {
    id <NSFetchedResultsSectionInfo> sectionInfo = [[self.fetchedResultsController sections] objectAtIndex:section];
    return [sectionInfo name];
}

Alternatively, you can define periodYear as transient attribute of the managed object. It will also not be stored in the database in that case, but can be implemented in a way that the value is calculated on demand and cached.

The DateSectionTitles sample project from the Apple Developer Library demonstrates how this works.

I recommend against using a transient property as the sectionNameKeyPath as it will result in faulting all objects obtained by the fetch request just so the property could be used as the section path.
You better define a persistent property of year and use it as your sectionNameKeyPath.
set you FRC sectionNameKeyPath to year like so:

[[NSFetchedResultsController alloc] initWithFetchRequest:fetchRequest
                                    managedObjectContext:self.managedObjectContext
                                      sectionNameKeyPath:@"year"
                                               cacheName:nil/*your chioce*/];

to display the section name as a title in the table, implement:

- (NSString *)tableView:(UITableView *)tableView titleForHeaderInSection:(NSInteger)section
{
    id<NSFetchedResultsSectionInfo> sec = [self.fetchedResultsController sections][section];
    return [sec name];
}