E 5” ] 
In the following inveftigations, 
Let a — Annuity, Rent, or Penfion. 
n ■==. Number of times that intereft is to be paid 
for the annuity, or fum lent. 
r = Rate of intereft of i f. for i time. 
»-o 
771 — Amount of the annuity, or fum lent for 
« times, at r intereft. 
p — Principal fum ufed, or prefent worth of a 
fum before it is due. 
Of Compound Intereft. 
Firft, In Amounts, 
Let q — i -\- r — Amount of i JT. for i time. 
Now, a — laft year’s amount. 
And„i : q :: a : aq — laft but one year’s amount, 
i : q :: aq : aq 1 = laft but two year’s amount, 
i : q : : aq 1 : aq 1 — laft but 3. 
And fo on to aq n ~ 1 = firft year's amount. 
. I - 
Therefore a aq aq 1 aq 1 6cc. -\- aq n ~ x — 771. 
But a: aqv.Tii — aq , '~ 1 : /;/ — a. Euc. 1 2. v. 
Then 771 — a — 7 nq — aq n 
Or 771 — a — m mr — acf 
Therefore aq" — a — 771 r Put A = q”. 
Then A — 1 x a = 7 nr 
Therefore A = ———■ 
Hence a = 
A — I 
_ A — 1 X a 
777 
A — 1 x a. 
: V tv; , . 'Vi \J 
i; 
Second, 
