298 Dr. Young’s for mu la for expressing 
years been very commonly admitted ; but its effects have not 
been so satisfactorily rectified as could be desired. 
In the 66th volume of the Philosophical Transactions, for 
the year 1776, we find a Paper of Dr. Price, in which he 
lays down these theorems, r denoting the interest of £1. for 
a year, and n the term or number of years during which any 
annuity will be paid, p the perpetuity, or j,y the value of an 
annuity paid yearly, and h half yearly : then, l,y=p — ; 
and, II, h —p — — — l - — — : and as examples, taking r =3 . 04, 
T+t) 
and w = 5, we have y = 4 . 4518, and/> = 4 . 4913 . 
Now, if we analyse the results thus obtained, by dividing 
them into the present values of the separate payments, they 
will stand thus : 
I. Present value of £1. payable at the end of) 
£. .961538 
1 year. 3 
2 years - 
- .924556 
3 years - 
- .888996 
4 years - 
- .854804 
5 years - 
- .821927 
4.451821 
II. Present value of 10 shillings, payable at the) 
end of half a year) 
£. .49020 
1 year 
- .48058 
It - - 
■ - .47127 
2 - - 
- .46192 
2t - 
- .45286 
3 - - 
- .44398 
3 f - 
- .43528 
4 - - 
- .42674 
4 f “ 
- - .41837 
5 - - 
■ - .41018 
4.49138 
