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CH A P. XII.

Of Compound Interest, and Annuities, &c. COMPOUND Interest is that which arises from any Princi.

pal and it's Intereft put together, as the Intereft fo'becomes due; so that at every Payment, or at the Time when the Pay-' ments became due, there is created a new Principal; and for that Reason it is called Intereft upon Intereft, or Compound Intereft.

. As for Instance; Suppose Tool were lent out for two Years, at 6 per Cent. per Annum, Compound Intereft: then at the End of the firft Year, it will only amount to 1061. as in Simple Interest. But for the second Year this 106 l. becomes Principal, which will amount to 1121. 7 s. 21 d. at the second Year's End, whereas by Simple Intereft it would have amounted to but 112 l.

And altho' it'be not lawful to let out Money at Compound Interest; yet in purchasing of Annuities or Pensions, &c. and taking Leases in Reverfion, it is very usual to allow Compound Interest to the Purchaser for his ready Money; and therefore it is very requisite to understand it.

Sect. 3. Of Compound Intereft.
= the Principal put to Interest,
= the Time of it's Continuance.

as before.
=the Amount of the Principal and Intereft. J
[R={

S the Amount of il. and it's Interest for 1 Year, at

I any given Rate, which may be thus found.
Viz. 100 : 106 :: 1 : 1,06=the Amount of il. at 6 per Cent. ;
Or 100 : 105, :: 1 : 1,05 = the Amount of il. at 5 per cent.
and so on for any other assigned Rate of Interest,
Then if R = the Amount of 1 l. for one Year, at any Rate.

R’ the Amount of 1 l. for two Years.
Rithe Amount of 1 l, for three Years.
R4=the Amount of r.l. for four Years,

RS=the Amount of il. for five Years. Here t=5 For 1:R::R:RR:: RR: RRR :: RRR: R4::R:R:&c.in ::..

As one Pound : is to the Amount of one Pound at one That is Year's End :: fo is that Amount: to the Amount of Lone Pound at two Year's End, &c.

Whence

: One P.

Whence it is plain, that Compound Interest is grounded upon a Series of Terms, increasing in Geometrical Proportion continued ; wherein t (viz. the Number of Years) does always affign the Index of the last and highest Term : Viz. the Power of R, which is R.

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Question 1. What will 2561. 10 s. amount to in seven years, at 6 per Cent. per Annum, Compound Intereft?

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Then 1: 0,06 :: 100 : 6 the Rate per Cens. required.

The first three Questions may be much more easily performed by the following Table, which is only, the Amounts of one Pound for thirty-nine Years,

That

That is, of R.RRRRR. R. RSand so on to R39.

Years 1.

1

Years.ums

Years 3.1

The Amounts The Amounts I The Amounts
of 1 l. at 6 per of 1 l. at 6 per of 1 l. at 6 per
Cent. &c. Com Cent. &c. Com Cent. &c. Com-
pound Interest. pound Intereft. pound Intereft.
1.06=R 2.2609039557 4.8223459407

1.1236 =RR 2.3965581931 | 28 | 5.1116866971
31.191016=R3

2.5403516847 29 5.4183878990 1.26247696

17 2.692772785730 5.7434911729 1.3382255776

2.8543391529 | 31 | 6.0881006432 1.4185191122 3.0255995021 | 32 | 6.4533866818 1.5036302590 3.2071354722 | 33 | 6.8405898828 1.5938480745

21 3.399563600534 | 7.2510252757 9 | 1.6894789590 221 2.6025324166 | 35 | 7.6860867923 16 1.7908476965 2313.8197496616136 8.1472519998 IT 1.8982985583 24 4.04893464131378.6360871198 32 2.0121964718 254.2918707197 389.1542523470 | 13 | 2.1329282601 | 26 4.5493829629 39 9.7035074878

00

20

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