EXAMPLES.

1. What principal will amount to £1045 143. in 7 years, at £6 per cent. per annum?

Ratio=06

Divisor 1.42)1045-7(736.4084+£736 8 2.

1045-7

Or,

·06x7+1

£736 8 2 Ans.

2. What principal will amount to £3810, in 6 years, at £41 per

cent. per annum?

3. What principal will amount to £666 9s. 01 £5 per cent. per annum ?

Ans. £3000.

in 31 years, at Ans. £563.

4. What principal will amount to £335 7s. 3d. in 3 years and 97 days, at £91 per cent. per annum ?

CASE IH.

Ans. £255 19 03.

The amount, principal, and time given, to find the ratio.

RULE.

Subtract the principal from the amount; divide the remainder by the product of the time and principal, and the quotient will be the ratio.*

EXAMPLES.

1. At what rate per cent. will £543 amount to £705 18s. in 3 years?

From the amount=705.9

Take the principal=543*

Divide by 543x5=2715)162.90(06

162.90

the same example, the amount, 33-6=30+30×06 × 2, or which is the same thing, 1+06X2X30. Divide both by the same quantity, 1+06×2, and the

expression will still be equal, and we have

; then

33.6 1+06×2×30 1+06×2 1+06×2 33.6 30, that is, the a1+06×2

cancel the equal terms in the last fraction, and

mount divided by the product of the ratio and time increased by 1, gives a quotient, which is the principal. The same may be shown in any other example, and, hence the rule is general.

* Under case I. it was shown that the amount, 336-30+30x06×2. Take the principal, 30, from both sides, and 336-30-30X06X2, or 3-6-30×2×-06. 30X2X.06 Divide both parts by the product of time and principal, and

3.6

30 X 2

30

3.6

or

=06, the ratio, and illustrates the rule,

2. At what rate per cent. will £391 17s. amount to £449 3s. 13d. 74qr. in 31 years? Ans. £4. 3. At what rate per cent. will £413 12s. 6d. amount to £546 4s. 101d. in 43 years?

Ans. £6.

4. At what rate per cent. will £3000 amount to £3310 in 6 years? Ans. £41.

CASE IV.

The amount, principal, and rate per cent. given, to find the time. RULE.

Subtract the principal from the amount; divide the remainder by the product of the ratio and principal; and the quotient will be the time.*

EXAMPLES.

1. In what time will £543 amount to £705 18s. at £6 per cent. per annum ?

From the amount=705.9
Take the principal 543

Divide by 543x06=32·58) 162.9(5 years, Ans.

1629

2. In what time will £3000 amount to £3810, at 4 per cent. per annum? Ans. 6 years. 3. In what time will £391 17s. amount to £449 3s. 13d. at £41 per cent. per annum ? Ans. 31 years.

To find the Interest of any Sum, at 6 per cent. per annum, for any

number of months.

RULE.

If the months be an even number, multiply the principal by half that number; and if the months be uneven, halve the even months, to which annex; thus the half of 19 is 9.5; and multiply the principal as before, dividing by 100 or cutting off two figures more at the right band, than there are decimals in both factors, which reduce to farthings, each time cutting off as at first.

4. What is the interest of £345 16s. 6d. for 9 years and 11 months, at 6 per cent. per annum ?

A Table of decimal parts for every day in the twelfth part of a year, which consists of 3651 days.

| days. \dec. pts.) days. dec. pts.| days, \dec. pts.\ days. dec. pts. days. \dec. pts.

4

131 10

⚫328 16 5 164 11 .361 17 558 23 756 29 .953 6 •197 12 .394 18 ⚫591 24 ⚫788 30 .986

⚫526

22

.723 28

.920

To find the Interest of any Sum, either for Months, or Months and Days at 6 per cent. per annum.

RULE.

Multiply the principal by the number of months, (or months and parts, answering to the given number of days in the table) and cut off one figure at the right hand of the product more than is required by the rule in decimals, and the product will be the interest for the given time, in shillings and decimal parts of a shilling.*

In the Note, under the General Rule for Simple Interest, it is shown that when the Rate is 6 per cent. the product of the principal and half the number of months divided by 100, gives the Interest. Whence, the product of the principal and the number of months divided by 100, must give twice the Interest. 30.5X17 Let then the principal £30.5 be put to interest for 17 months. Then 100

=£5.185=2× £2.5925=twice the interest, and the interest is 2-5925. Multiply by 20 and the interest will be reduced to shillings and the decimal parts of 30.5 X 17X20 a shilling, and we have =2×£2·5925 × 20. Divide by 2, and 30-5X17X10

100

30-5 × 17

10

100

-=£2.5925×20, and dividing both parts of the fraction by 10,

-=£2·5925 × 20, that is, multiply the principal by the number of months and divide the product by 10, or, cut of only one figure more than the rule for

Kk

EXAMPLES.

1. What is the interest of 2. What is the interest of £250 10s. for 19 months and 7

£ 100, for a year?

Principal 100

Another Method of calculating Interest for Months, at £6 per cent.

per annum.
RULE.

If the principal consists of pounds only, cut off the unit figure, and, as it then stands, it will be the interest for one month in shillings and decimal parts :--If it consist of pounds, shillings, &c. reduce the shillings, &c. to decimals, which, with the unit figure of the pounds, will be decimal parts of a shilling.*

decimals requires, and you have the interest in shillings and decimal parts of a shilling. If there be months and days, the days being made decimals from the table, the same rule would manifestly apply.

This rule is only a contraction of the following process by the Double Rule of Three, to find the interest of any sum, e. g. £36, for 1 month.

As 100 6 :: 36

12×100

the interest in shillings, or shillings and decimals, and cancelling the equal parts, 6X36×20 1×36×2

we have

12×100 2×10

1x36×1 36
1 × 10 10

36 shillings. If there be fie

cimals of a pound, the rule would be equally correct

SIMPLE INTEREST IN FEDERAL MONEY.
PROBLEM I.

When the principal is given in New England pounds, shillings, &c. and the annual interest is required in federal money, at 6 per cent.

RULE.

Reduce the shillings, &c. to their equivalent decimal, by inspection, divide the whole by 5, and the quotient is the annual interest: Or, multiply the principal by 2, and the product (having the unit figure of the pounds cut off) will be the interest as before.*

EXAMPLES.

1. Required the annual interest of £517 3s. 74d. at 6

per

D. c. m.

cent.?

103-436=103 43 6 Ans.

Excess of 12=001

2. Required the annual interest of £1, in cents?

PROBLEM II.

Ans. 20 cents.

When the principal given in New England currency, and the interest and amount are required in federal money at 6 per cent.

RULE.

Reduce the New England money to federal, then divide the principal by 20 and that quotient by 5; add those quotients together, and they are the interest; or add them to the principal, and their sum is the amount.

EXAMPLES.

1. Required the amount of £425 16s. 81d. for 1 year, at 6 per cent.?

* This rule is a contraction of the following process. By the General Rule 517-181X6 for Simple Interest, (in the first example) the annual interest= 100 This, multiplied by 20, would be reduced to shillings and decimals of a shilling, and divided by 6, would be reduced to dollars and decimals of a dollar. Then, 517·181×6×20 517-181X1 517-181

$103 43c. 62 m.

5

+ Dividing the principal by 20, gives the interest at 5 per cent. because 5 is one twentieth of a hundred; then dividing this quotient by 5, evidently gives the interest for 1 per cent. Then, as 5-+1=6, the sum of the two quotients will be the interest at 6 per cent.

Interest at 6 per cent. may often be calculated most easily, by finding the interest at 5 per cent. and adding one fifth of this interest to itself for 6 per cent. And add two fifths of it to itself, and you have the interest at 7 per cent.