Chapter 3, Life Contingencies Stationary Population problems (T)

Daniel_Plasterer@tiginsurance.com
Thu, 4 Mar 1999 14:07:49 -0500

Fall 1992 #20: A ranch shows horses in competition and maintains a
constant herd size of 1,000. New horses enter at exactly age 5. No horse
leaves the herd prior to age 20 except by dying. All horses who reach the
age of 20 are immediately sold. Each year 100 horses die before reaching
age 20, at average age 12.

Determine how many horses are added each year using the Parmenter (AAD)
method.

AAD= x + Tx - Tx+n - nlx+n
lx - lx+n

I understand how the book came up with x=5, n=15 and lx-lx+n = 100, but
the part that I'm stuck on is Tx-Tx+n = 1,000.

Can someone please explain to me why Tx-Tx+n = the constant size of a
stationary population?

I understand that Tx is the total future lifetime of those aged x in the
population and Tx+n is similarly defined, but why is it that you can
subract the two and come up with the number in the population?

Any insight will be appreciated.

Dan