CHAPTER III

ASSURANCES, SINGLE PREMIUMS

1. The value now of one payable for certain at the end of n years at interest rate i per annum is (1+i)-n=vn=A,-,l.

The value now of one payable at the end of n years if a definite event should happen is v" multiplied by the probability that the event will happen.

For example,

The value now of one payable at the end of one year if (x) should be alive at the end of the year is

vpx =v 1x+1 =A 1

l   II'

The value now of one payable at the end of one year if (x) should die within the year is

vgx =v dx =A'T

The value now of one payable at the end of n years if (x) should be alive at the end of the n years is

v,h „nt'x =vn lx+xn =A

x--' The value now of one payable at the end of n years if (x) should die within the n years is

v"•=v"(1—,,px)=Awl —Axn1=Ax .

The value now of one payable at the end of n years if (x) should die in the nth year from now is

v” • n—1 I Qx =vn dx+n—1 =vn lx+n—1 —vn lx+n =vA x ~ 1 —A 1 lx   lx   lx   x nl '

2. The value now of one payable at the end of the year of the death of (x), i.e., payable on the first anniversary of this date to which he does not survive, is written Ax