COMPOUND Interest

, called also Interest upon Interest, is that which is reckoned not only upon the principal, but upon the interest itself forborn, which thus becomes a sort of secondary principal.

If r be the amount of 1 pound for 1 year, that is the sum of the principal and interest together for one year; then is r2 the amount for 2 years, and r3 the amount for 3 years, and in general rt the amount for t years; that is rt is the sum or total amount of all the principals and interests together of 1l. for the whole time or number of years t; consequently, if p be any other principal sum, forborn sor t years, then its amount in that time at compound interest, is .

The Rule therefore in words is this, to one pound add its interest for one year, or half year, or for the first time at which the interest is reckoned; raise the sum r to the power denoted by the time or number of terms; then this power multiplied by the principal, or first sum lent, will produce the whole amount.

For example, To find how much 50l. will amount to in 5 years at 5 per cent. per annum, compound interest.——Here the interest of 1l. for 1 year is

.05, and therefore r=1.05 ; hence the 5th power
of it for 5 years, is r5=1.27628 &c;
multiply this by p or-        50
gives the amount prt or 63.814l.
or 63l. 16s. (3 1/4)d. for the amount sought.

But Compound Interest is best computed by means of such a table as the following, being the amounts of 1 pound for any number of years, and at several rates of compound interest.

As an example of the use of this table, suppose it were required to sind the amount of 250l. for 35 years at 4 per cent. compound interest.

In the column of 4 per cent, and line of 35 years, is3.94609,
which multiplied by the principal250 
gives986.52250 
or986l 10s (5 1/4)d,
which is the amount sought.

Note, By a bare inspection of this table, it appears how many years are required for any sum of money to double itself, at any rate of compound interest; viz, by looking in the columns when the amount becomes the number 2. So it is found that at the several rates the respective times requisite for doubling any sum, are nearly thus: viz,

Rate33 1/244 1/256
Years23 1/220 1/417 3/415 3/414 1/412
TABLE of the Amount of 1l. at Compound Interest for many Years and several Rates of Interest.
Yrs.at 3 per centat 3 1/2 per centat 4 per centat 4 1/2 per centat 5 per centat 6 per cent
11.030001.035001.040001.045001.050001.06000
21.060901.071231.081601.092031.102501.12360
31.092731.108721.124861.141171.157631.19102
41.125511.147521.169861.192521.215511.26248
51.159271.187691.216651.246181.276281.33823
61.194051.229261.265321.302261.340101.41852
71.229871.272281.315931.360861.407101.50363
81.266771.316811.368571.422101.477461.59385
91.304771.362901.423311.486101.551331.68948
101.343921.410601.480241.552971.628901.79085
111.384231.459971.539451.622851.710341.89830
121.425761.511071.601031.695881.795862.01220
131.468531.563961.665071.772201.885652.13293
141.512591.618691.731681.851941.979932.26090
151.557971.675351.800941.935282.078932.39656
161.604711.733991.872982.022372.182872.54035
171.652851.794681.947902.113382.292022.69277
181.702431.857492.025822.208482.406622.85434
191.753511.922502.106852.307862.526953.02560
201.806111.989792.191122.411712.653303.20714
211.860292.059432.278772.520242.785963.39956
221.916102.131512.369922.633652.925263.60354
231.973592.206112.464722.752173.071523.81975
242.032792.283332.563302.876013.225104.04893
252.093782.363242.665843.005433.386354.29187
262.156592.445962.772473.140683.555674.54938
272.221292.531572.883373.282013.733464.82235
282.287932.620172.998703.429703.920135.11169
292.356572.711883.118653.584044.116145.41839
302.427262.806793.243403.745324.321945.74349
312.500082.905033.373133.913864.538046.08810
323.575083.006713.508064.089984.764946.45339
332.652343.111943.648384.274035.003196.84059
342.731913.220863.794324.466365.253357.25103
352.813863.333593.946094.667355.516027.68609
362.898283.450274.103934.877385.791828.14725
372.985233.571034.268095.096866.081418.63609
383.074783.696014.438815.326226.385489.15425
393.167033.825374.616375.565906.704759.70351
403.262043.959264.801025.816367.0399910.28572
413.359904.097834.993066.078107.3919910.90286
423.460704.241265.192786.351627.7615911.55703
433.564524.389705.400506.637448.1496712.25045
443.671454.543345.616526.936128.5571512.98548
453.781604.702365.841187.248258.9850113.76461
463.895044.866946.074827.574429.4342614.59049
474.011905.037286.317827.915279.9059715.46592
484.132255.213596.570538.2714610.4012716.39387
494.256225.396066.833358.6436710.9213317.37750
504.383915.584937.106689.0326411.4674018.42015

COMPOUND Motion, that motion which is the effect of several conspiring powers or forces, viz, such forces as are not directly opposite to each other: as when the radius of a circle is considered as revolving about a centre, and at the same time a point as moving straight along it; which produces a kind of a spiral for the path of the point. And hence it is easily perceived, that all curvilinear motion is compound, or the effect of two or more forces; although every compound motion is not curvilinear.

It is a popular theorem in Mechanics, that in uniform compound motions, the velocity produced by the conspiring powers or forces, is to that of either of the two compounding powers separately, as the diagonal | of a parallelogram, according to the direction of whose sides they act separately, is to either of the sides. See Composition of Motion, and Collision.

Compound Numbers, those composed of the multiplication of two or more numbers; as 12, composed of 3 times 4. See Composite.

Compound Pendulum, that which consists of several weights constantly keeping the same distance, both from each other, and from the centre about which they oscillate.

Compound Quantities, are such as are connected together by the signs + or-. Thus, a + b, or a-c + d, or aa - 2a, are compound quantities.

Compound quantities are disting uished into binomials, trinomials, quadrinomials, &c, according to the number of terms in them; viz, the binomial having two terms; the trinomial, three; the quadrinomial, 4; &c. Also, those that have more than two terms, are called by the general name of multinomials, as also polynomials.

Compound Ratio, is that which is made by adding two or more ratios together; viz, by multiplying all their antecedents together for the antecedent, and all the consequents together for the consequent of the compound ratio. So 6 to 72 is a ratio compounded of the ratios of 2 to 6, and 3 to 12; because : also ab to cd is a ratio compounded of the ratio of a to c, and b to d; for . See COMPOSITION of Ratios.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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COMPARTMENT
COMPARTITION
COMPASS
COMPASSES
COMPOSITION
* COMPOUND Interest
COMPRESSION
COMPUTATION
CONCAVE
CONCAVITY
CONCENTRIC