( *12 ) 
greater ; and in Fee Simples it vanilhes; the contrary to which 
happens in Amounts of Sums of Money, and Annuities. 
All which is propos’d to be re&ify’d, only by a juft re- 
dutftion of the Rate, and Annuity; ( which is done by de- 
ducting fo much per Cent, thereout, as the whole Trouble, and 
Charge of Management is fuppos’d to amount to, and redu- 
cing the Remainder, by a Difcount equivalent to the fuppos’d 
lofs of time) and then by working with the Rate fo reduc’d, 
for Sums of Money, and with the Rate and Annuity reduc’d 
in the like proportion for Annuitys, according to the common 
Method of Compound Intereft; as follows. Fut r for the 
rate of Intereft of i l.c for the Charge and Trouble of the Ma- 
nagement of i /. Then is r — er — the Rate after deducing 
the faid Charge, = (putting d for i — c ) dr. And for the 
Difcount put t for the time loft, that is for fuch part of the 
Period of time in which the Payments are made (whether 
Yearly, ~ Yearly, Quarterly, or otherwilej as is fuppos’d to 
be Ipent in receiving and putting them out again at Intc- 
reft. Then, d/r, being — the Intereft of i /. for that time; 
dr 
fay, as l 4 ~ dtr : i : : dr : J — -- = (putting e for 1 -f dtr ) 
1 x dtr 
dr 
, which is equal to the reduc’d Rate, near enough for 
e 
pra&ice, for which put £. But if the utmoft accuracy be re- 
quir’d, the Difcount itfelf muft be made with regard to the 
like lofs of time, which is done by a Series of Difcounts rais’d 
1 ✓ , td z r z tdr 1 t'dr' , 
thus;r( = l ~r tdr): tdr:: dr: :: : 
e t e* 
td % r t 1 d 3 r 1 f d* / 
Whence dr — - — - q- &c. —f putting q for 
e e 1 c J 
1 dr -- ; ■ d r 
) 1 — 4 1 — tf&c* * dr. = — ( =1 “ q xdr)^r q 1 — q i &c. 
c e 
* dr, is = t, == the ti;ue Rate reduced. Put s = 1 -f- n — 
! l he time, p = the prefent Sum or Value, m = the Amount. 
Then 
