C 5*2 3 
Second, In Difcounts. 
Since q 1 1 :: a : — = ift year’s prefent worth. 
q: i 
q:i 
:: — : p = 2d year’s prefent worth. 
And fo on to 
a 
r 
-=. zzth years prefent worth. 
Therefore ± + 4 4- 4 &c. to - == *. 
9 4 9 9 n 
But — : 4 — - — : p — — • Euc. 12. v» 
q q 1 q n q 
Therefore /’f' ~~ _f. — pq — a. 
qn t 1 
Or Pqn ^— =zp Ar pr — a. 
Therefore aq n — a 
Or A — 1 x £ = />rA. 
Therefore A = — - — 
a — rp 
Hence A — 1 x a = mr = prA. 
Therefore A = — = — - — = — = 1 4 - r, 
a a — rp p * 
Cafe I. Given a> m> p\ Required r. 
Jince A 
P 
Therefore r =: * ■ * 
m 
Cafe II, 
