SIMPLE INTEREST.

ART. 107. The relation between the principal, time, rate per cent., and interest, is exhibited to the eye in the diagram on the opposite page. Let the single line A (which for convenience is separated from the diagram, but which should be considered as extending horizontally to the left from B, C, D, etc., respectively,) represent the principal; the perpendicular line BG represent time with its divisions into years, at the points C, D, E, and F; and the horizontal lines CH, DI, EK, FL, and GM the accrued simple interest at the expiration of each successive year. As no ratio can be expressed between time and money, area can represent nothing in the diagram. As rate per cent. is nothing but the ratio between the principal and interest, it can only be represented by the degree of divergence of the lines BC and BH, by which the lines CH, DI, EK, and FL shall bear a proper relation to the line A. If the rate be 10% per annum, the line CH must be or of the line A, DI, EK, and so on. The line BM represents nothing but a limit to the lines representing interest for any time on the line BG. A+CH, A+DI, A+EK, etc., represent the amount due each successive year at simple interest.

ART. 108.

ANNUAL INTEREST.

Simple and annual interest are the same for the first year. At this time in "annual interest," the accrued simple interest on the principal forms a new principal to draw simple interest till maturity. The same is true at the end of each following year. This increase of interest will be represented by the lines I1, K3, Lo, and M... The rate being 10%, I must be of CH its principal; K3= of CH+1% of NI= of CH; of OK of CH; and M1.=

Le=% of CH+NI+

6

10

10

6

1 of CH+1% of NI+13% of OK+;% of PL=}; of CH=CH. It will be observed that the line B1. is not a straight line, but composed of straight lines, the degree of divergence from the line BG being increased at the end of each year; also that the numbers 1, 3, 6, 10, etc., are the sums of the several series 1;

ita; itatɔ; 1+2+3+, etc.; and also that they express

1

2

3

4,

the number of years that the simple yearly interest of the principal must draw interest to equal the interest on all the several amounts of annual interest. The line ab, though limited by the straight line is still a correct representation of the interest due at the end of 4 years with annual interest.

6, 109

ART. 109.

COMPOUND INTEREST.

Annual and compound interest are the same for two years. Then the interest which has accrued on the first annual interest becomes a part of the principal. In like manner all the interest at the end of each year becomes a part of the principal for the next year. The line 1, c, d, a, limits the horizontal lines representing compound interest after the first two years. It should be separated from the line B1, at the point 3, a distance equal to of I. At the point ., a distance equal to зc+ of Kc. At the point,

At the point 10, equal to ed+ of Ld.

Or, comparing simple interest with compound, the line B2 must begin to diverge from the line BM at the point H, and be separated from BM at the point I, a distance equal to of CH. At the point K, equal to the I1+ of D1. .At the point L, equal to Kc+ of Ec. At the point M, equal to Ld+' of Fd.

“PARTIAL PAYMENTS"
" ILLUSTRATED.

ART. 110. The Diagrams on the following pages illustrate the difference in the principle of the three foregoing rules for "Partial Payments."

The problem used in each diagram is the following:
A note for $1000 runs 4 years with interest at 6%.

In 1 yr. from date a payment of

In 14 yrs. from date a payment of.
In 2 yrs. from date a payment of

$50 is made.

250
224

In 2 yrs. 8 mo. from date a payment of

In 2 yrs. 10 mo. from date a payment of.
What was due at maturity?

In the illustration, time is measured horizontally by the distance between the perpendicular lines.

The horizontal base line in each figure separates principal from interest, the perpendicular lines above representing the former, and those below the latter. The perpendicular lines above are limited by a horizontal line which is more or less removed from the base line, as the payments are applied to increase or decrease the principal. The perpendicular lines below, representing interest, are limited by a line always diverging from the base line, the degree of divergence depending upon the rate per cent. and the size of the principal. When the entire interest is cancelled by any payment, the diverging line starts anew from the horizontal base line. The perpendicular distance between these two limiting lines at any time represents the amount of principal and interest due at that time.