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.