1000000030

N T

3nlt r;\tc.

ui(~

fvur

prvul~:1t~ ; r~~r

IJ?\·:ng all1 threc

of rhefe,

rh~

flltlllh nl1y"I\"..

a~s h~ r~lIncl .

,Thus,

Probo V. Il.r\'i"ci rhe pri!lc;p,,!, rime, ano rare, tO

find rhe anlú,"I(.

Rule: r'¡".J rhe in:mll by probo 1. add it to the

principal, the fum ;s rile

amo~nr .

Thus , by·prob.

rhe inrm:1is

t'r :

rherefore the

amollO(

a=pl(+p.

Thc reafon is e,iJenr.

Nute : 13:c,rufe

plr:::rIXp,

and

=IXp

th~re·

fore

rlp+p:=rl+IXp=.1.

And fo rhe rule mal' be

exprdl~J

rhus ; To

th~

proJlItl of the rm

~nd

time

adJ uniry, and multiply the fut.l by the principal, the

produtl is the amount.

EX1m?le: What is the amonnt of 2461. principal

in 2

ycm

.nd

or 2.

yem,

theme of intere{l being

.Oí

Anfl'ler 2461.+ 30.7S I.=276 1. tss. for the

interell iS=2 .¡6X.oSX2.S= P. 7SI. Or rhus ;

.0SX

~ . S=. 12 51.

to wl,ich add

it is 1+.1251. wh,ch

muhiplied by 276, produces 276.75 1.

ProJ. VI. Giveo the

prin~ipal,

amount, and time,

find lhe rateo

Rule: Take lhe diITerence betwixr the principaland

amount, and

dil'id~

ir by rhe produ"! of rhe time and

¡incioal, t:,: quote is the rate : th.s,

r=°-P,

Ex.¡m?k: Suppofe

0=276 .75 1. P.=246, 1=2. 5

years

then is

r=.05

1.=2 76·75-~ 46_30·7 S

2 ' 5X~466'i5'

DClllon{lrarion: Since by probo V.

o=lrp+;,

take

from both {ide', it is

a-;=Irp

theo divide borh

o-p

Ip,

H IS

-¡¡=r.

Probo

VII.

Given the amOllnr, princ!pal, and rate,

to find rhe time.

Rule: Take rhe di[ erence of rhe amount and prin.

cipal, and diviJeir by rhe prodllél of rhe princ' pal and

rale, rhe quote is the rime: thus

I=tt-P.

Examplc: Sup?o[e

0=176.75

1. /,=246 1.

r=.05 ;

then is 1=2 ·5 YW¡=27 6· 75I.-Z.1Ó

iO.75

.05

t23'

Dc:nonllration: In the lall prcblem,

n-p

was e·

qual to

Irp

;

and dividing both

rp,

it is

o-p

=1.

Probo VIII. Given rheamounr, rare, and time, to

find the principal.

uk: .'¡dd r rO rhe

prvJuL~

of the rate and time,

~od

by thu [um divide the amount, t1,e quote is the

. . I h

pnnclpa : t us,

p= rl+ l'

Example. n=1 76.75 1. r= 051.

l=z .5

years; then

;¡

' 6¡::~

27 6 .75

_.1 7

6 '75 .

/' 'l

05+1

D~ll\~n{lrat;on :

By plob.

.~ri·¡:~

X·p;

thcnfure

dividln~

:'or h fi dLs by

1'1+ 1,

it is--n_=p.

1'1+1

CO"'I'~lml l

'TER FST,

is rhnt IIhich is paid for any

in–

clpal fum, anu d"

I,nl~k

inrcrcll C:u;

up~n

101'

nny

N T

time,

nccullluldl~d

ir,roon:

prin~ip¡1 f~nt.

E):aml'!c :

loo

1. is lent

OUI

fol' Ooe rear ar 61. ar.J if

rhe

cnd of rhat y,ar the 61. dueof in!erc!!

adJcJ tO the

principal, anJ the fUlll t061. be confidcrcJ as a new

principal belring intml\ (or the next year (or what–

ever le[s time ir remains unpaid) this is calleJ com–

pounJ intmfl, becau!"e there is interdl upoo intere/!,

which mal' go on byadJing rhis [econd rear's interell

of 106 1.

rhe principal 1061. and making

th~

whole

a principal for rhe next year.

Now, alrhough it be n rlawful to let out money at

compound inrere{l, yer in purchafing of aonuirics or

penr.ons,

&c.

and taking leafes in re'

·err.on

, it is very

ufu.1 to allow compound inrerell to the purchafcr for

his ready

mon~y;

and therefore, it i, ver)' nece{fary ro

under{land it.

Let therefore, as

b~fore,

p=the principal put

io–

terell; I=rhe time of irs conriouance

o=rhe amount

of rhe principal and intcrell; R=rhe amouot of 11.

and its inrerd! for one year, at any given rare, which

mal' be thus fouod.

Viz ,

100: 106:: ( : I,oi\=the amount of 11. at

6per Ctnl.

Or 100: 1°5:: 1: 1,05=theamountof

1. ar

"nI.

And fo

00,

for any other afligncd

m e of iotere!!.

Then if

=amo~nt

of 11. for

yen, at .oy rate,

R.'=an,cunt of

fur 2 years.

R'=amount of

for

rears.

R'=amount of

for

years.

R'=amcur.t of 11. for 5years.

Here

1=5.

Forl : R :: R : RR :: RR:RRR::

RRlt ::R' : R·I: :R' :

uc.

in agcomerrica! progreflioD

continued; rhar is, as 11. : is to rheamounr of

1. at

years's end: : fo is thar amount : ro the amount of

at 2 years end,

&c.

"'hence ir is plain, that como

pound inrerell is ground,J upon a feries of terms,

increafing in beommical proponion cominued; whm·

in 1

(,'i:.

the numberof ycatS) does always aflign rhe

indcx cf rhe lall and highc{l rerm,

viz.

rhe power of

R, which is R'.

Again, as

1 :

R':

:p:pR' =O

rhe amounr of

for

the rime, that

= rhe amount of

1. That is, as

11.: is tO rhe amount of

1. for any giren rime :: fo

is any propofed principal, or furo: to irs amount forthe

fame rime.

From what has been faid, we prefume, ¡he mfon

of the folJowings ,hcorenrs wilJ be

VCI

y eafi!y ueJer–

llood.

Theorcm

1. /'

R'=. , as abore.

Fronr hence rhe rlVO foll,¡wing theorems are eafily

d~duced.

Theorem

11.

·it'='"

Theorem

'::'=R'.

By rh.'fe

.Ime

thlorcml, all r,ccfli,'ns a"om con,.

po"nJ in.('rdl mal' ue uuly

Il l~h'<d

u, dl< p'" cnly,

,:0.

wirlwur tabl,,:

dWllgh

lI<n fo ,,·.JI!y as l'y ,l'e

hdp

c-f

l u~'!'~ c,lkul ~~

!'~rj'l,ft·.