SIMPLE INTEREST BY DECIMALS.

A Table of Ratios, from one pound, &c. to ten pounds.

| Rateper cent. | ratios. | rate per cent. | ratios. | rate per cent ratios

Ratio is the Simple Interest of £.1 or D. for 1 year, at the rate per cent. agreed 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. I decimal parts. | days | decimal parts.

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.

EXAMPLES.

1. Required the amount of £.537 10s. at £.6 per cent. per annum, for 5 years?

Principal

The following Theorems will fhow all the poffible cafes of Simple Interest: Where p principal, t-time, r-ratio, and a amount.

a

a-p

I ptr.+pa. II.- p. III. IV.

tr+1

a-p

τῇ

Or, 537.5×·06x5+537•5=£.698 15s.

2. What is the simple interest of £.917 16s. at £.5 per cent. per annum, for 7 years? Ans. 321 47.

3. What is the amount of £.391 17s. at £.44 per cent. per annum, for 34 years?

Ans. .449 3 12. 4. What is the amount of £.235 3s. 9d. at £.54 per cent. per annum, from March 5th. 1784, to November 23d. 1784 ?

Ans. £.244 0 84. 5. If my correspondent is to have £.2 per cent; what will his commission on £.785 15s. amount to? Ans. .19 12 105

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 8, and the amount=4.572 9 8.

7. If a broker disposes of a cargo for me, to the amount of £.637 10s. on commission at £.14 per cent. and procures me another cargo of the value of £.817 15s. on commission at £.13 per cent.; what will his commission, on both cargoes, amount to ? Ans. £.22 5 7.

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.

EXAMPLES.

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

Ratio='06

Multiply by the time 7

Product=42

Add 1.

Divisor 1.42)1045-7(736-4084+ £.736 8 2.

+=

1045.7

Or,

.736 8 2 Ans.

-06x7+1

2. What

2. What principal will amount to £.3810, in 6 years, at £.4 per cent. per annum ?

Ans. £.3000. 3. What principal will amount to £.666 9s. 04 in 3 years, at .54 per cent. per annum ?

4. What principal will amount to £.335 7s. 97 days, at £.9 per cent. per annum?

CASE III.

Ans. £.563.

3d. in 3 years and 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 L.705 18s. in 5 years? From the amount=705.9

Take the principal-543

Divide by 543x5=2715) 162.90(.06

705·9-543

Or,

=06=£.6 Ans.

543x5

162 90

2. At what rate per cent. will £.391 17s. amount to

12d. 74qr. in 34 years?

.449 3s. Ans. £.4.

3. At what rate per cent. will £.413 12s. 6d. amount to .546 4s. 101d. in 4 years?

Ans. £.64.

4. At what rate per cent. will £.3000 amount to £.3810 in 6 years?

CASE IV.

Ans. .4.

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. 1d. at £.4 per cent. per annum ? Ans. 3 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 pricipal by half that number; and if the months be uneven, halve the even months, to which annex; thus the half of 19 is 95; and multiply

2...G

the

the principal as before, 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 ?

Y. m.

9 11 12

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

consists of 3654 days.

days | dec. pts. | days | dec. pts. | days | dec. pts. | days | dec. pts.

days dec. pts.

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

EXAMPLES.

Another Method of calulating Interest for Months, at 61. per cent. per annum. RULE.

If the principal consist 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.

When the principal is given in Massachusetts pounds, shillings, &c. and the in terest is required in federal money, at 6 per cents per annum.

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.

J. Required the annual interest of 5171. 3s. 74d. at 6 per cent.?

2. Required the annual interest of 11. in cents?

5)1.00

20 cents, Ans.

PROBLEM II.

When the principal is given in Massachusetts old currency, and the interest and amount are required in federal money at 6 per cent.

RULE. Reduce the Massachusetts 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.