Corrected algorithm below:

But what you really want is when you'll be a billion seconds, so lets see how many days a billion seconds is:

minutes = 1,000,000,000 / 60 = 16,666,666 min 40 secs
hours = 16,666,666 / 60 = 277,777 hr 46 min 40 sec
days = 277,777 / 24 = 11,574 days 1 hr 46 min 40 sec
years = (11,574 / 365) - 8 = 31 years, 259 days, 1 hr 46min 40 sec

So 259 days from June 17 (Julian date is 31 + 28 + 31 + 30 + 31 + 17 = 168)
Day offset = 365 - 168 = 197 days
Day offset 2 = 251 - 197 = 54 days

Your Billion second birthtime = Feb 23rd, 2006 at 03:46:40