Missing payments. If you don't see a recent payment you've made, make sure you've allowed enough time for the payment to post to your account: Payments made by electronic check, by credit card, at a T-Mobile store, or over the phone usually post to your account right away, but it can take up to three hours.
Nothing in-game uses Kerbin days/years as far as I can tell. A day is defined as 86400 seconds, and a year as 365 days.
The Cosmic Year. The Cosmic Calendar is a scale in which the 13.7 billion year lifetime of the universe is mapped onto a single year. This image helps to put cosmology, evolution, and written history in context. At this scale the Big Bang took place on January 1 at midnight, and the current time is mapped to December 31 at midnight. At this scale, there are 434 years per second, 1.57 million years per hour, and 37.7 million years per day.