S36 
€>F INTEREST AND ANNCrTlES. 
Thus, because PR n is — g, there will come out P 
a l— 
-^-„and R = -jLj "> &c. or by, exhibiting the same 
equations-in logarithms (which is the most easy for prac 
tice) we shall have 
1°. Log. a — lag. P + n x lag. R. 
2A Log. P. — log, a — n x log. R. 
3 n . Log. R. = '°g- a - log - P -. 
„ _ log- * — log. P 
4 • iogTTl. 
Which four theorems, or equations, serve for the four 
cases in compound interest. 
A x —— i 
Again, since m is rz -—^ —, we shall have 
r i°. Log. m = log. A + log. R* — l — log. R — 1. 
; 2°. Log. A. = log. m — log. R” — l + log. R — I- 
3°. u 
_ log. wR — m f A — log. A 
4\ R” 
log. R 
wR m 
s~ + x — 1 - 
To which the various questions relating to annuities 
in arrear are referred. 
I : - 
- - 1 "ppi . 
Moreover, seeing A x — is=v, we thence have 
l 
i°. Log. v = log. A f log. i 
I 
11« 
log. R — i. 
2°. Log. A = log. v -f log. R— i — log. j L. 
R* 
log. A — log. A + v — ?R 
n — 
log. R 
4®. R ? *+ 1 - A + l x R’ 1 | A r ft 
- ’ v - ff • - • ' v •