I get 38.66 billion years, when using an object 13.799 billion light years away. I wrote a little code to calculate it and used an expansion rate of 73 km/sec per megaparsec, and recalculate the expansion rate for every 10,000 years (since it would increase as it got further away).

But I know that must be wrong because thats based on an object being 13.799 billion light away... 13.799 billion years ago and expanding at 73 km/s per mpc for the past 13.799 billion years..

So how do you calculate this?