Yousuf Khan wrote:

Isn't it possible that given only what we can observe, we will always
come up with a finite age for the universe, and it will always be the
same age limit no matter when we do the calculation? For example if
we're calculating the age of the universe to be somewhere around 15-20
billion years old now, then a 100 billion years from now another set of
observers will look at what they can see in the universe at that time,
and they too will come up with 15-20 billion years rather than 115-120
billion?

We estimate the age of the universe to be about 13.7 billion years.
As the universe expands faster and faster, our observable horizon
will begin to shrink and we will no longer be able to "see" the early
universe.

No Center
http://www.astro.ucla.edu/~wright/nocenter.html

Also see Ned Wright's Cosmology Tutorial
http://www.astro.ucla.edu/~wright/cosmolog.htm
http://www.astro.ucla.edu/~wright/cosmology_faq.html

WMAP: Foundations of the Big Bang theory
http://map.gsfc.nasa.gov/m_uni.html

WMAP: Tests of Big Bang Cosmology
http://map.gsfc.nasa.gov/m_uni/uni_101bbtest.html