1822] Mr. Adams on Compound Interest. 455 
= present value of the perpetuity of 1/. per annum, the interest 
payable m times in a year. 
Art. 23.—If in Art. 19, be infinite, then will + x 
beget = present value of the perpetuity of 1/. per annum, 
r ew 
e) =" 
when the annuity is payable u times in a year, and the interest 
m times. : : ps 
For a fuller account on this subject, and for a variety of inte- 
resting and useful examples, see Mr. Francis Baily’s “ Doctrine 
of Interest and Annuities.” a: 
From the preceding articles, the state of the population of a 
country under given circumstances may easily be determined. 
If in any place where there is no migration, and. the increase 
of population observe the following law, the amount of the whole 
penpion at any given time may be determined as follows : 
et P represent the population of a country at any given period ; 
= = B = number of births, and : = D = number of deaths in 
prep ht pi tag 2 ; 
a year, then will a ica — _P =.B— D = increase of 
population in the first year; from whence = = a Ne: 
Now if in Art. 1, for principal, we write populanon, for r we write 
e, and for s we put A, we shall have P (1 + e)" = A = popu- 
lation at the end of years; therefore, 
1 (1+e".P=A, 
A 
II. G+ee = BR 
AY 
I. (5) -l=e 
1 At. P 
IV. a ae x 
If m P = A, then will (1+e)" =m, from whencen =1.m 
—1.(1 +) = a period in which the population would be 
increased m times. die 
If the population decrease, we shall have > — > = oS eS 
a ab 
D — B = decrease of population in the first year, from whence 
as e'. By substituting in Art. 5, we get (l—e')*. 
P = A' = decrease of population in # years ; therefore, 
7 
