ii6 Dr, price’s Theorems 
life, will be 13,829 + ^^=14,043. If fecured by land 
and payable half-yearly, its value will be 14,01 o+- | Q 4 - 
= 14,1 17. If fecured by land and payable quarterly, its va- 
lue will be 1 4, 1 o 1 + — ’— = 1 4, 1 5 5 . The like values in 
the fecond example are 9,065, 9,130, and 9,151. 
Life-annuities payable monthly or weekly may be 
confidered as of the fame value with annuities payable 
momently ; and it is evident, that they muff be enjoyed 
nearly to the laft moment of life. 
From thefe rules and examples it may be gathered, 
that the difference between the values of annuities 011 
lives payable yearly, half-yearly, quarterly, and mo- 
mently, increafes continually with the ages ; but, if not 
fecured by land, this difference can never be fo great as 
a quarter of a year’s purchafe in the cafe of annuities 
payable yearly and half-yearly ; three-eighths of a year’s 
purchafe in the cafe of annuities payable yearly and 
quarterly ; and half a year’s purchafe in the cafe of an- 
nuities payable yearly and momently. 
Mr. Simpson, in his Treat ife on the Dodlrine of Life- 
annuities, p. 7 8. and in his Select Exercifes, p. 283. hath 
given a quarter of a year’s purchafe as the addition al- 
ways to be made to the value of a life-annuity payable 
yearly, in order to obtain its value payable half-yearly; 
and three-eighths of a year’s purchafe, if its value paya- 
ble quarterly is required. But it appears, that thefe are 
too large additions; and, whatever be the rate of intercff, 
6 
or 
