Ruby convert decimal duration (day|week|month|year) to end date - ruby-on-rails

Question

I have a start_at, a decimal quantity and an interval which is one of day | week | month | year.
start_at = Time.parse('2016-01-01 00:00:00 UTC') # leap year
quantity = BigDecimal.new('1.998') # changed from 2.998, should end on 2/29/16 sometime
interval = 'month' # could be any of day|week|month|year
With whole numbers, I've used duration i.e. 1.month, and I looked at Date#advance, though it only recognizes integer values.
It would seem simple but I cannot find anything in the standard libraries or in ActiveSupport.
References:
SO answer potentially used for input to Date#advance?
SO explanation of duration
Question
How can I establish the end_at date from a decimal?
Why? What purpose?
Proration to the second for a given amount and given interval.
Expectations
I'm looking for an end_at to the second as accurate as possible with respect to advancing the next interval(s) by the decimal quantity. Given interval = 'month', for the fractional part, when you pass the start of the month, means you are in that month and using it's duration. For example, January 2016 is 31 days, while February (leap) is 29 days (only in the leap year).

Answer 1

I'd say your best option is to use Ruby's date methods to advance time based on the whole number of the decimal, then calculate how many seconds your fraction is of your current interval.
So for 1.998 months, advance time 1 month. Find the current month you are in and get the .998 of the seconds in that month (i.e. for July, 31x24x60x60x.998) and then advance time that many seconds.

Answer 2

What does advancing time a fractional month mean?
Lets say we have the following date 2015-01-01 00:00:00 UTC. It is easy to advance exactly 1 whole month, we simply increment the number that represents months: 2015-02-01 00:00:00 UTC. Alternatively, we could view this as adding 31 days, which we know is the number of days in January.
But what if we want to advance 0.5 months from 2015-01-01 00:00:00 UTC?
We can't just increment like we did when advancing a whole month. Since we know January has 31 days, perhaps we could just advance 15.5 days: 2015-01-16 12:00:00 UTC. That sort of works.
How about 1.5 months from 2015-01-01 00:00:00 UTC? If we combine our previous approaches, we'd first increment, getting us to 0.5 left to advance and 2015-02-01 00:00:00 UTC. Then we'd take half of 28 and get to 2015-02-15 00:00:00 UTC.
But wait, what if instead we took the total number of days between the two months and then took 3/4 of that? Like 2(month) * (3/4), which would simplify to (3(month)) / 2, or 1.5(month). Lets try it.
(28 days + 31 days) * 0.75 = 44.25 days
Now adding that to 2015-01-01 00:00:00 UTC we get 2015-02-14 06:00:00 UTC. That's three-quarters of a day off from our other answer.
The problem here is that the length of a month varies. So fractional months are not consistently definable.
Imagine you have two oranges. One contains a little bit more juice than the other (perhaps 31ml and 29ml of juice). Your recipe calls for the juice of 1.5 oranges. Depending on which one you decide to cut in half, you could have either 44.5 ml or 45.5 ml. But if your recipe calls for 40 ml of orange juice, you can pretty consistently measure that. Much like you can consistently (kind of) increment a date by 40 days.
Time is really tricky. We have leap seconds, leap years, inconsistent units (months), timezones, daylight saving time, etc... to take into account. Depending on your use case, you could attempt to approximate fractional months, but I'd highly recommend trying to avoid the need for dealing with fractional months.