1 N T

I N T

Whence 'as plain, That Compoundgrounded upon a Rank of Geometrical Prop°nals continued; the last of which is known yNumber signified by (<) and is

Secondly, 11 : /t f : : P Ergo P - ‘ *

n That is, As on<; Poim d : Is to the Amount of one

p °und fa my time proposed : '• So ts I<5 > IO °.’ , ’

» Sum proposed: To its Amount, ft the ffrnetine. x 1

r eilt ^p 1 two Proportions, the General Thco-

thav k °~ ^ sufficiently demonstrated, and

clearly understood.

Qwest, i Suppose 250 1. hath been at Interestfe-ffTearj . IVhat doth it amount to, at 6 perc nt. per Annum, Compound Interest.

t»

CrciS given P =250/. t = 7, and a — 1.06.

^ 0r loo : 6 :: 1 : 1,06 =r a the first Year:

Th

-7 - 1 c w if (i be involved so often, until its Indexit a 1 — at - and then multiplied into P,

k at " produce sj, as appears by the Theorem

g ^ ?.

f\ a — 1.06, involved 7 times =2 1.50363.

• j-l * 5 o x 115036$ = 375 - 9‘°75 — K-front lS> 375 /• 18 s. 2 d. is the Sum producedV Cj( . l d' 0 7. having been at Compottnd-Interest sevenS > sos above proposed.)

2. Suppose 375 1. 18 S. 2 d. were to be paidJoven Tears hence ; What is it worth in readyWoncy, abating 6 per Cent. per Annum, Com-pound Interest.

Is given tx — 375.9075. t — 7 , and a => lo find P.

ene ta! Theorem is, P a * ~ ?, therefore ^ =2 P.

J) 7 1,7 A t

, c ^ 1.06 and involved 7 times — 1.50363.nd 75.9075^— __p. t fi at i s> worth25o/.

I ’5°jd3\. ready Money.

3. Suppose 250 1. hath been at Interest,ad e Amount is 375 1. 18 s. 2 d. at 6 per Cc°m pound Interest ; How long hath it btlorborn ?

a 5 Cre « given, P = 250, K ~ 3?5-9°75, ^dd c r for one Year; thence to hnd t, the In-C * °i the Power of a.

G ?

nt (al Theorem, P a* ~ Ergo, p' — a 1 .

C ° nse quently if a * be continually divided by a,

I'fii it become " — 1, the Number of such Di-

dif^ s "fill be t : For such Number of Divisions'’Ors how ©ft a was Involved.

But 375-9°75f_ ,.^363 = ^

250 N

= 1.418518-

1.06 v

Also 1.338125.

1.06 >

I

And so on, till it become ' , (= r, which will

be at the seventh Operation.

Then will t — 7, the Number of Years requi-red.

Quest. 4. Suppose 2 5 o 1. hath been forborn sevenTears, and the Debtor is willing to give up bothPrincipal and Interest, proffering 375 1.1 8 s. 2 d.to be cleared ; What ffjte of Interest per Cent.{allowing Compound Interest) doth he hereby offerto the Creditor.

Here you have given P — 250, ^ 375.9075,and t — 7, to find a.

General Theorem, P a* — Ergo p — a ( .That is, a f =: at, consequently y — a

r

But p (= 1.50363Let a — r -\- e.

Then r 1 -|- 7 r A e 21 r f e e 2=2 a 1 ~G.

4 r 1 ~|- r 6 e -I - 3 r< c e — ~ G.

. . *G

y r r -j - r e 3 ft = “.

G

r e -}- 3 e e =2 —j — 4 r r — D,

D

Hence this Theorem, —-2= e,

r 3 e

Let r — 1

1.50363 2= G..214804 —4 G I- r ! .— .142857 — 4 rr

.071947 222 D (.06 =: e.708

Divisor — 1.18 .21480428 — 46.

.16051432 —46 1 ,-r.First r — 1 —.16051428.

-J- e == .06 . -

- .000000004

New r — 1.06 — a

Then 1 : 1.06 :: 100 : 6 — the Rate of the In-terest required.

But if in any Questions, either of Interest or An-nuities, the time given or sought, be not termina-ted by whole Years, but by Weeks, Months,Quarters, Half-years, Three Quarters, G?c. for re-solving such Questions, first reduce such broken orFractional Parts of the Year into Days, vi%. T 1 —7 Days, -!- = 3°-4 Oays, — 91.25 Days, | —182.5 Days, i — 273.75 Days, and so for any oddNumber of Days that falls betwixt such even Partsof the Year.

This done, find an Answer, according to theDemand of the Question (and agreeing to onePound as before) for the Number of the Days pro-posed.

To perform which, it will be requisite to resolvethis following Question.

Y y y 1

What

5