You should really use NSCalendar and NSDateComponents for calculations like that since they can get very tricky and can be full of annoying edge cases.
If you use NSCalendar and NSDateComponents (like the code below) it will take care of all the things like leap years for you.
NSDate *now = [NSDate date];
NSDateComponents *minusHundredYears = [NSDateComponents new];
minusHundredYears.year = -100;
NSDate *hundredYearsAgo = [[NSCalendar currentCalendar] dateByAddingComponents:minusHundredYears
toDate:now
options:0];
I've written about working with dates in Objective-C general if you want some extra reading on the subject.