Is there a simple way to do tiered coin rounding using standard Cocoa libraries? - cocoa-touch

Question

In 2012, Canada abolished the 1¢ penny. To allow cash transactions to be processed at a 5¢ resolution, the following rounding policy was put into place:
The calculation of the Goods and Services Tax (GST) or Harmonized Sales Tax (HST) on purchases, whether for cash or non-cash transactions, will continue to be calculated to the penny and added to the price. It is only the total cash payment for the transaction that will be rounded.
From Royal Canadian Mint.
That is, all calculations should be done as accurately as possible and end up using standard "round half-up tie breaking to achieve hundredths resolution, but when it comes time to make the cash payment, further rounding to the nearest nickel is required.
For internationalization, I need to implement this. I also would like to re-use this for other places where, say, the final cost is rounded to 10¢, 25¢, etc. How do I accomplish this behavior in iOS, using NSDecimalNumbers?
I'd love if it worked like this on Obj-C:
finalCost = [total roundWithResolution:#0.05];
or this in Swift:
finalCost = total.roundWithResolution(0.05);
To clear up any ambiguity above, this is the behavior after having already rounded to the hundredths place using "round half-up" tie breaking:
5¢
$0.98 to $1.02 → $1.00
$1.03 to $1.07 → $1.05
$1.08 to $1.10 → $1.10
And so on
10¢
$0.96 to $1.05 → $1.00
$1.06 to $1.15 → $1.10
And so on
25¢
$0.88 to $1.12 → $1.00
$1.13 to $1.37 → $1.25
$1.38 to $1.62 → $1.50
$1.63 to $1.87 → $1.75
$1.88 to $2.12 → $2.00
And so on

Answer 1

Took me a night's worth of asking around and testing solutions, but I finally came up with this:
#implementation NSDecimalNumber (RoundWithResolution)
- (NSDecimalNumber *)roundWithResolution:(NSDecimalNumber *)resolution
{
NSDecimalNumber *step1 = [self decimalNumberByDividingBy:resolution];
NSDecimalNumber *step2 = [step1 round:0];
NSDecimalNumber *step3 = [step2 decimalNumberByMultiplyingBy:resolution];
NSDecimalNumber *step4 = [step3 round:2];
return step4;
}
- (NSDecimalNumber *)round:(NSUInteger)decimalPlaces
{
NSNumberFormatter *formatter = [NSNumberFormatter new];
formatter.roundingMode = NSNumberFormatterRoundHalfUp;
formatter.numberStyle = NSNumberFormatterNoStyle;
formatter.maximumFractionDigits = decimalPlaces;
return [NSDecimalNumber decimalNumberWithString:[formatter stringFromNumber:self]];
}
#end
This is based off this formula on Math.SE by kccu, Milo Brandt, and Eric Towers: