C 494 ] 
A comparifon of the refill t of the before going inve /li- 
gation of the ‘value of an annuity for life ( fecured 
by land J, with the value thereof given by Mr. De 
Moivre, in p. 67. of N° 4 73. of the Philofophical 
Tranfa&ions. 
If the annual payment, or rent, be fuppofed to be 
1 /. ; if the rate of intereif (that is, the amount of 1 /. 
and its intereft for one year) be denoted by r ; the 
number of years which the annuitant may poffibly 
live (called by Mr. De Moivre the complement of life) 
by n ; and the value of an annuity of 1 1 . per annum y 
certain for n years, by P : Then, by Prob. I. of Mr. 
De Moivre’s treatife of annuities on lives, the value 
of an annuity (not fecured by land) for the life of a 
1 — -P 
perfon, whofe complement is n, will be — ; to 
which if — be added, thefum 
2 n 
-P 
— + — will, 
-i 2 n 
according to the refult of the above inveftigation, be 
the value of an annuity (fecured by land) for the life 
of the fame perfon : And if the hyperbolic logarithm 
of r be denoted by a ; then, by the above-quoted 
Philofophical TranfaSiion , — 
will be the 
1 an 
value of the fame annuity, according to Mr. De 
MQivre : Let us proceed, therefore, to examine, whe- 
ther 
