n 
Then Will I -f- — q'&c.xdr X^I -j- pi 
be exa&Iy — m : But 14 
dr 
And for the Amounts and pre 
* 
X P = m is fufficient for pra&ice, 
"ent values of Annuitys. 
Put A Annuity per annum. 
<* = Annuity •; yearly, quarterly,^. 
R — Yearly rate of Interell; of 1 /. 
r = Rate ^yearly, quarterly, &c. 
r •— Reduc’d rate yearly, f yearly, quarterly, 
n — Number of Years, years, quarters, &c. 
r t 
Then will be — reduc’d Annuity taken yearly 
f yearl y, qua rterly, or other wife ; and by Compound Intereft 
c 1 -i -rl— 1 1 
r R ~ 
twill be — ^ * a — = 
t. r 
s' — 1 
. s n — i m 
A — m, and - — A( — ) 
R R s' s' 
p- Whence the 
Theorems for folving all the other Cafes are eafily deduc’d. 
And if the Rate be requir’d, when ’tis for a Sum of Money, 
the Solution is obvious • when for the Amount or Value of 
. . - mr A- a a 
an Annuity, fince i 4 -r, n — — arethe Equa- 
tf a — pr 
tions whence Theorems for the Rate are ulually deriv'd, which 
by this Corre&ion become \ -j- rh = ~ 4 — — - That 
a a — pr . 
the fame £ may be had on both Tides the Equation, put //£ 
for r 9 and ’twill be 1 4-rj" = 
m 
ut-j-a 
a 
: then,, by 
? a y a ■ — put 
the Rate auum’d as near the truth as may be, find the value 
1 1 s 
of u ( == — 4- 1 r =~ — and in any Theorem for the 
