166
LIFE ASSURANCES.
of insurance, by the chance of the given life or lives surviving that term,
then multiply the difference between the product thus found and unity,
by the present value of £l due at the end of one year; from this result
subtract the product obtained by multiplying the present value of a tem
porary annuity for the same term as the assurance by the difference
between unity and the present value of £l due at the end of a year.
By Davies’s method—
(2) From the number opposite the given age in column M subtract
the number in the same column opposite the age as many years older
as the insurance has to continue, and divide the difference by the num
ber in column D opposite the age of the party at the present time.
Or thus (3) : From the number in column N opposite the age one
year younger than the given life, subtract the number in the same
column opposite the age one year younger than the life will be at the
expiration of the term of the insurance; multiply the difference by tbe
present value of £l due at the end of one year; from this product sub
tract the difference between the number in column N opposite the
present age and the number in the same column opposite the present
age increased by the number of years the insurance is to continue, and
divide by the number in column D opposite the present age.
202. To find the annual premium.
Rule. When the single premium is known, add unity to the present
value of an annuity for the term of the assurance diminished by the
present value of the last payment of this annuity, and divide the single
premium by the result.
When the single premium is not known divide by the same result
the difference between unity and the present value of £l to be received
at the expiration of the term of the assurance, provided the given life
or lives survive that term, and from the quotient subtract the difference
between unity and the present value of £l due at the end of a year.
By Davies’s method—
203. From the number in column M opposite the present age, sub
tract the number in the same column opposite the age increased by the
number of years for which the insurance is effected, and divide the
result by the difference between the number in column N opposite the
age one year younger than the present, and the number in the same
column opposite the present age increased by one less than the number
of years for which the insurance is made ; or,
204. Find the difference between the number in column N oppo
site the present age and the number in the same column opposite the
age increased by the number of years for which the insurance is effected,
and divide this quantity by the difference between the numbers in the
same column opposite ages respectively one year less than these last,
and subtract the quotient from the present value of ¿£l due at the end
of one year.