I have a contract that was signed on Nov 4, 2016. It says that we can cancel the contract within three business days from the above date. Additionally, it also says "To cancel this transaction, mail or deliver a signed and dated copy of this cancellation notice to" followed by an address and "no later than midnight of Nov 9, 2016". I am wondering if midnight of Nov 9 means a minute after Nov 8 11:59PM or it is after Nov 9 11:59PM.
The drafter of the original contract crated the problem by use of the phrase, "midnight of Nov 9".
The instant of midnight is not "of" any one day. It is the dividing line between two days, and is not uniquely part of either one.
I have seen phrasing like, "midnight of Nov 9 - 10" which refers unambiguously to a specific time.
Coincidentally, I received my annual car insurance policy renewal today (Toronto, Canada). Upon checking the policy , I discovered that the policy is in effect on 15 Dec 2016, and the expiry date is given as "15 Dec 2017 at 12:01 AM" In other words, the insurer has given me a free minute of insurance, just to avoid the "midnight" ambiguity.
It's not quite obvious whether "midnight" is in the very early morning or late at night, although I would tend to assume it means late in the night and that might be the legal meaning.
However, since they wrote the contract and chose the words, and not you, if it went to court the ambiguity would have to be resolved in your favour. If you wrote the contract and chose the words, and "midnight" were deemed to be ambiguous, then it would be interpreted in their favour.
Unless the contract defines midnight otherwise, it takes on its ordinary meaning: 00:00am (that is, one second after 11:59:59 PM).
Having said that - 00:00 could equally be represented as 24:00 (and thus belonging to the previous day.
Both of your interpretations are valid, and without more context, it would be ambiguous and interpreted in favour of the party who did not draft the contract ("contra proferentem").
You signed on Nov 4 at NM:ZY hours, and you can cancel the contract if you do so in 72 hours or less before NM:ZY of Nov 7. Now they can charitably allow you a few hours until the next midnight, since the deadline is expressed as days and not hours, but that gets you to only the 7th-8th boundary, not the 8th-9th boundary. You don't need to know whether that is on or of the 7th or 8th: it is in fact right now, and maybe too late depending on your time zone. The correct reading can be derived, obscurely, from the four corners.