[ i°9 ] 
VI. Short and eafy 'Theorems for finding , in all cafes , the 
Differences between the Values of Annuities payable 
Yearly , and of the fame Annuities payable Half-yearly , 
Quarterly, or Momently . the Rev. Richard Price, 
Z>. Z). P. R. S . //* # Letter to Sir John Pringle, Bart . 
P. P. A 
R * 1*775’ r F lHE values of annuities, as given in all the 
common tables, fuppofe them paid yearly. 
Rut it is well known, that generally they are paid half- 
yearly, and fometimes quarterly \ and that this is a cir- 
eumitance which always adds to their value. The 
difference between the values of annuities, according as 
they are paid in thefe different ways, I have feen no 
where Rated with accuracy ; and therefore, I have thought 
that the following attempt to do this may be of fome 
ufe. 
Annuities are of two forts. They are either payable 
certainly or conditionally. Of the former fort are all an- 
nuities which are payable at fixed times, without de- 
pending on any contingency. Of the latter fort are all 
annuities on lives. I will firft confider the firft fort of 
annuities. 
Let r denote the interefl of if. for a year; and n the 
term or number of years during which any anuuity is to 
a be 
