Excersise 4.5.b needs to find the derivative of the n-Year Term pure
endowment (which is very hard to write in this word processor). The
formula for this is (v^n)(npx). This is:
d(v^n)(npx) npx d(v^n) v^n d(npx)
----------- = ------ + ------
dn dn dn
(npx)(D)(v^n) + (v^n)(-npx Mx+n)
= (v^n)(npx) (D - Mx+n)
= (n-Term pure end.) (D - Mx+n)
where D is the force of interest (delta) and Mx+n is the force of
mortality (mu)
What totally annoys me is that the answer in the book implies that this
final result (the derivative to respect of n of the N-year pure end.) has
a D + Mx+n, instead of D - Mx+n
Does anyone think this a defective question --o answer?
BTW, just as a reference, I used the equation 3.2.20 in page 50, that
says:
d tpx
----- = - (tpx)(Mx+t)
dt
Thanks!