1 1 2 
Dr. price’s ‘Theorems 
In the foregoing theorems it may he obferved, that 
the ratio to one another, of the values of annumes paya- 
ble yearly, half-yearly, quarterly, and momently, is 
created: when n is lead; that it decreafes continually 
as n increafes, till at lad it vanidies, when n becomes in- 
finite or the annuity is a perpetuity. Agreeably to this 
it appears, in the examples I have given, that the values 
in the fird example differ more from one another in 
proportion than the values in the fecond example; and 
that thefe alfo differ more than the values in the 1 tnr , 
and that in the lad example all the values are nearly t te 
UU Thefe values computed by Mr. de moivre’s rules in 
his Treatife on Life-annuities, p. 86. and 1 24, See. come 
out greater when n exceeds, and lefs when « falls rort 
of j c or 20 years. But thofe rules fuppofe the half- 
yearly and quarterly intereds of money to be lefs than ha 
or a quarter of the yearly intered. For indance ; the va- 
lue of an annuity of i£. payable half-yearly and quar- 
terly for so years is, according to Mr. de moivre s rules, 
„ 1,699 and 21,77*. or a 99* part and 74 * more 
than the value of the fame annuity payable yearly, fup- 
pofing money improved at 4 per cent, when the annuity 
l paid yearly; and at £.1,98 percent, when it is paid 
half-yearly; and at 0,985 per cent, when it is paid quai- 
terly : That is; fuppofing money improved at a rate of 
half-yearly or quarterly intered, which, indeacl ot being 
a half or a quarter of the yearly intered, is only fit at 
