but that the price had been increased in the course of
a few years from eleven years' purchase to twelve, and from twelve to
fourteen. He also states that the rate of interest had been
successively reduced from 6-1/4 to 5%, and then to 4%. The principal
object of his report is to prove that, taking interest at 4%, a life
annuity was worth at least sixteen years' purchase; and, in fact, that
an annuitant purchasing an annuity for the life of a young and healthy
nominee at sixteen years' purchase, made an excellent bargain. It may be
mentioned that he argues that it is more to the advantage, both of the
country and of the private investor, that the public loans should be
raised by way of grant of life annuities rather than perpetual
annuities. It appears conclusively from De Witt's correspondence with
Hudde, that the rate of mortality assumed as the basis of his
calculations was deduced from careful examination of the mortality that
had actually prevailed among the nominees on whose lives annuities had
been granted in former years. De Witt appears to have come to the
conclusion that the probability of death is the same in any half-year
from the age of 3 to 53 inclusive; that in the next ten years, from 53
to 63, the probability is greater in the ratio of 3 to 2; that in the
next ten years, from 63 to 73, it is greater in the ratio of 2 to 1; and
in the next seven years, from 73 to 80, it is greater in the ratio of 3
to 1; and he places the limit of human life at 80. If a mortality table
of the usual form is deduced from these suppositions, out of 212 persons
alive at the age of 3, 2 will die every year up to 53, 3 in each of the
ten years from 53 to 63, 4 in each of the next ten years from 63 to 73,
and 6 in each of the next seven years from 73 to 80, when all will be
dead.

De Witt calculates the value of an annuity in the following way. Assume
that annuities on 10,000 lives each ten years of age, which satisfy the
Hm mortality table, have been purchased. Of these nominees 79 will die
before attaining the age of 11, and no annuity payment will be made in
respect of them; none will die between the ages of 11 and 12, so that
annuities will be paid for one year on 9921 lives; 40 attain the age of
12 and die before 13, so that two payments will be made with respect to
these lives. Reasoning in this way we see that the annuities on 35 of
the nominees will be payable for three years; on 40 for four years, and
so on. Proceeding