Let  us  now  compute  the  present  value,  to  an  insurance  company,
of  $1  to  be  paid  by  each  of  a  group  of  69,804  persons  50  years  old,
now  and  at  the  beginning  of  each  year  hereafter,  so  long  as  any  are
living.  The  total  value  of  $1  from  each  of  them  now  is  obviously
$69,804.  Only  68,842  are  living  a  year  from  now,  so  only  $68,842
is  paid  the  company.  This  $68,842  is  due  a  year  hence,  so  we
discount  it  for  one  year  and  68,842  X  $0.970,874  =  $66,836.91  is
its  equivalent  present  value.  Similarly,  $67,841  will  be  paid  the
company  two  years  hence  by  those  who  become  52  years  old.
This  sum  discounted  for  two  years,  or  67,841  X  $0.942,596  =
$63,946.66,  its  equivalent  present  value,  etc.  At  this  point  is
given  a  table  showing  the  steps  already  outlined  for  the  whole
of  life,  to  be  followed  by  an  explanation  of  the  further  steps.
26


NOTES   ON   LIFE   INSURANCE.
Calculation  of  Present  Value,  based  on  the  American  Experience
Table  and  3  per  cent,  interest,  of  $1  paid  now  and  at  the  beginning
of  each  year  of  life  by  each  of  a  group  of  69,804  persons  50  years
old  and  their  survivors.
YEAR.
Attained
age  at
beginning
of  year.
(i)

Present  value
of  $1  to  be
paid  certainly
at  begin
ning  of  years
indicated.
(2)
Tabular
number  living
at  begin
ning  of  each
year.
Product  of    (1)X(2).
Present  value  of  sum  to
be  received  by  com
pany    in    each    year.
