A note given 18th August, 1804, for

Interest to 19th March, 1805, 213 days, $19-352

Paid 19th March, 1805,

$540

19.352

559.352

50

19. A owes B the following sums, with interes! at 6 per cent. per annum $60 for 7 months, $150 for 9 months, $75 50 for 3 months, $365-25 for 8 months, and 510-20 for 5 months: Required the amount?

20. A note for $1000 is given January 1, 1803, with interest at 6 per cent. per annum; February 19, 1803, $100 are paid; June 7, 1803, $150; April 14, 1804, $37-50; July 11, 1804, $75; Sept. 29, 1804, $250; Dec. 17, 1805, $39; March 4, 1806, $175 ; Ang. 7, 1806, $105; Oct. 30, 1806, $50; May 12, 1807, $40, and Nov. 17, 1807, $72: How much is due, January 1, 1209?

SIMPLE INTEREST BY DECIMALS.

A TABLE OF RATIOS, FROM ONE POUND, &C. TO TEN POUNDS.

Ratio is the Simple Interest of £1 or $1 for 1 year, at the rate per cent. agreed on, and is found by dividing the rate by 100, and reducing it to a decimal. Thus, 106, and, 105, and so on. A TABLE for the ready finding of the decimal parts of a year, equal to any number of days, or quarters of a year.

Days. | decimal parts. | days. | decimal parts. | days.

dec. parts.

1027397

100 | 273973

200

•547945

008219

30

·082192

010959

40

•109589

⚫013699

50

•136986

of a year=25

016438

60

•164383

of a year=5

019178

70

•191781

of a year=75

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

RULE.

Multiply the principal, time and ratio continually together, and the last product will be the interest, commission, brokerage, &c. to which add the principal, and the sum will be the amount.

This is a contraction of the General Rule for Simple Interest. If the interest on £30 or $30 was required for 2 years at 6 per cent. by the general rule, 30x6 the interest is -X230X X2-30X 06X2, which is the product of. 100

6 100

principal, ratio, and time. And the amount=304-30x 06x2=£33.6 or $,

cent. per annum,

EXAMPLES.

1. Required the amount of £537 10s. at £6. per

for 5 years?

2. What is the simple interest of £917 16s. at £5 per cent. per annnum, for 7 years?

Ans. £321 4 7.

3. What is the amount of £391 17s. at £41 per cent. per annum, for 31 years? Ans. £449 3 12.

4. What is the amount of £235 3s. 9d. at £5 per cent. per annum, from March 5th, 1784, to Nov. 23d, 1784 ?

Ans. £244 0 81. 5. If my correspondent is to have £2 per cent; what will his commission on £795 15s. amount to? Ans. £19 12 101.

6. What will be the interest and amount of £445 10s. in 3 years and 129 days, at £8 per cent. per annum ?

Ans. Interest, £126 19 81, and the amount £572 9 8. 7. If a broker disposes of a cargo for me, to the amount of £637 10s. on commission at £1 per cent. and procures me another cargo of the value £817 15s. on commission at £13 per cent; what will his commission, on both cargoes, amount to? Ans. £22 5 7. 3. What is the simple interest of $66-666 for 12 years at 7 per Ans. $8 16c. 6m.

cent.? 9. Find the amount of $1 for 9 years and 200 days, computing interest at 7 per cent.? Ans. $1 66c. 8m. 10. What is the interest of $236 at 5 per cent. for one year and 500 days?

11. Required the interest on $6485 at 6 per cent. for two years, six months and 20 days.

CASE II.

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

RULE.

Multiply the ratio by the time; add unity to the product for a divisor, by which sum divide the amount, and the quotient will be the principal.*

In the demonstration of the Rule for Case 1. it was proved that the amount = the principal added to the product of the principal, ratio, and time, or, taking

EXAMPLES.

1. What principal will amount to £1045 14s. in 7 years, at £6 per cent. per annum?

Ratio='06

Divisor 1.42) 1045·7(736.4084+= £7368_2.

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

Ans. £3000.

3. What principal will amount to £666 9s. O in 3 years, at £5 per cent. per annum ? Ans. £563. 4. What principal will amount to £335 7s. 3d. in 3 years and 97 days, at £9 per cent. per annum ? Ans. £255 19 02.

CASE III.

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 5 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+30x06 × 2, or which is the same thing,=1+06×2×30. Divide both by the same quantity, 1+06×2, and the

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, 33-6=30+30x06×2. Take the principal, 30, from both sides, and 33-6-30-30 X 06×2, or 3.6=30×2×·063.6 30×2X.06 Divide both parts by the product of time and principal, and 30X2

3.6

or

30X2

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?

4. At what rate per cent. will £3000 amount to £3810

Ans.

£63.

in 6 years? Ans. £4.

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 543x-06-32-58) 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. 1 d. at £4 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 hall 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 hand, 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?