Numerical Solutions to Sample Test Problems
===========================================
(INCLUDES corrections)

1. (a)  > 1e5*(1-1.06^(-3))/(1-1.06^(-20))
[1] 23304.54
   (b) > (1e5-23304.54)*1.06^3*(1.06^(1/12)-1)
[1] 444.6289

2. (a) mu(t) = 5/(80+t)
   (b) integral from 0 to infty of sqrt(t)*1e4*5*80^5/(80+t)^6
> integrate(function(t)  sqrt(t)*1e4*5*80^5/(80+t)^6,0,Inf)$value
[1] 38416.96

3. > ((1+.06/4)^8*exp(.01*3+.01*(5^2-2^2)))^.2-1
[1] 0.07446384

4. (a) .75-.5/.9 = .1944
   (b) .9 + (20/30)*(.9*.75-.9) = .75