JR Pass Activation & Expiration

Hello, I will be staying in Japan for three weeks but not sure if I should get the 14 days or 21 days since my last week will be in Tokyo which I don't think I need a JR pass. Here is my itinerary:

April 3rd - Arrival date at Tokyo and go to Osaka.
April 4th - Osaka
April 5th - Osaka
April 6th - Osaka
April 7th - Hiroshima/Osaka (Day trip)
April 8th - Kobe/Osaka (Day Trip)
April 9th -13th - Kyoto
April 14th -15th - Nara/Kyoto (Day trips)
April 16th - 24th - Tokyo

I was thinking about getting the 14 day pass since I will be returning to Tokyo on the 16th. So if I activate the JR pass on April 3rd does that mean the pass will expire on April 16 at 11:59 pm?

Thanks!
Ansel