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

Mult. by the months=12

Ans. s.1200 £6

Note. This Table may also be used for the parts of a year, in Compound Interest, after having worked for whole years. The shillings, &c. in the principal must first be reduced to the decimal of a pound.

days?

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

pėr 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: :: 1 month: the interest.

6X36

6×36×20

Hence

£18-36s. the interest for 1 month. But

12X100

12X100

the interest in shillings, or shillings and decimals, and cancelling the equal parts. 6X36×20 1X36X2 1X36X1 36 1X 10 10

we have

12×100 2× 10

36 shillings. If there be de

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 cent.? 38.=.15 5)517-181

7 d. 030

Excess of 12001

D. c. m.

103-436 103 43 6 Ans.

Or, 517-181

103-4362=103 43 6.

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

PROBLEM II.

Ans. 20 cents.

When the principal is 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. 8d. 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, 517-181X6X20 517-181X1 517-181 $103 43c. 6.2.m. 100 × 6 517-181X6X20 517-181X1X2 517-181X2

Or

=

100×6

5X1

10x1

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 54-16, 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 3 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.

1504 61701504 61 7. Ans.

2. Required the amount of £112 4s. 6d. for one year?

Ans. $396 52c 7m. 9dec.

PROBLEM III.

When the principal is New England currency, and the monthly interest is required in federal money.

RULE.

Reduce the shillings, &c. to decimals, by inspection, then separate the right hand figure of the pounds with the decimals, divide by 6, and the quotient is the answer in dollars, cents, &c.*

EXAMPLE.

Required the monthly interest of £425 16s. 8d. in federal mo

HAVING PARTIAL PAYMENTS ENDORSED.

As there is much diversity of opinion relative to the computation of lawful interest in these cases, several Rules will be given, connected with the practice of the Courts of several of the States. The difference of the rules depends on the principle assumed in respect to the time when interest becomes due.

RULE I.

The following rule is generally thought to allow too little interest. It is, however, adopted in some of the States.

Find the amount of the principal and interest for the whole time; then find also the amount of each endorsement for the time it has been paid. From the first amount deduct the sum of the amounts of the several endorsements, and the remainder is the balance due. This rule involves the following points:

1. Interest is not due until the obligation is paid.

This rule is a contraction of the following process.

425-835X1X1 425-835-42-5835 1X10X6

the monthly interest in dollars and decimals of a dollar.

10X6

2. Hence, interest must be allowed on the endorsements from the time they were severally made.

Note. A shorter method of computing interest according to this rule, may be seen in examples 16 and 17 of Simple Interest. The absurdity of this rule may be seen in the following manner. Suppose I borrow $100 at 6 per cent. for ten years, and pay six dollars at the end of each year, what will be due at the end of 10 years? The amount of $100 is $160. But the first endorsement of $6 has borne interest for 9 years; the second, for 8 years; the third, for 7 years, and so on; so that six dollars have in fact been drawing interest for forty five years, and thus produced $16.20 of interest. This, added to the nine endorsements of $6 each, gives $70-20. That is, while I have paid only the annual interest of $6. the principal has actually been reduced $16.20. By paying $6 annually for 25 years, and computing interest on the several endorsements by this rule, the whole principal would be paid, and the lender would be indebted to the borrower the sum of $2, while in fact the lender had received no part of the sum lent.

RULE II.

The following rule was drafted by the late Judge Sedgwick, and ordered by the Court of Common Pleas for the County of Berkshire in 1791, and is the Rule now used by the Courts of Massachusetts.

"On all contracts carrying interest, on which partial payments may have been made, the principal sum with the interest thereof shall be formed, at the time of payment, into an aggregate sum, from which shall be deducted the sum paid, if one year's interest shall have become due, and if not, then the interest shall be cast to the end of the year, and the aggregate formed as aforesaid, and from the same the payment or payments and the interest thereof from the time or times of payment shall be deducted, and the balance or balances thus formed shall bear interest, and so from time to time, provided, that in no instance, interest shall be cast on a greater sum than the principal sum nor on any interest accrued." [Records of the Court.]

This rule involves the following principles. 1. That, when an obligation has borne interest for one or more years, interest is not due at intervals of time less than one year.

2. Interest is to be computed to that endorsement, which, together with the preceding endorsement or endorsements and its or their interest since the time of payment, shall be equal to or exceed the interest on the principal when this endorsement is made, provided one year's interest shall have accrued. The remainder is a new principal, on which interest is to be computed as before.

3. Interest is allowed on all endorsements from the time of their payment, until the year has elapsed, or until an endorsement is made beyond the year, which with the preceding endorsement or endorsements and its or their interest, equals or exceeds the interest due at such endorsement.

4. Interest is not allowed on interest, because the deduction, when made, is intended to pay the interest then due, and the excess, if any, goes to reduce the principal.

5. The design of the rule is to give the interest as nearly annially as the endorsements will admit. But if endorsements are not made on the obligation, the rule implies that the interest is not due until the obligation is paid; and, it is well known, that the Courts will not sustain an action for the payment of the interest from year to year, unless the obligation contains the express condition that the interest shall be paid annually.

Note. In the "Scholar's Arithmetick," and in the "Mercantile Arithmetick," the Rule, said to be established by the Courts of Massachusetts, is precisely the same as that established in the State of New York, which will be found on a following page. It will be evident from a comparison of the preceding Rule and that of New York, that the computation of interest ought to be considerably dif ferent in the two States.

RULE HII.

The following Rule was established by the Superior Court of Connecticut in 1784.

"Compute the interest to the time of the first payment, if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total. If there be after payments made, compute the interest on the balance due to the next payment, and then deduct the payment as above; and, in like manner from one payment to another, till all the payments are absorbed; provided, the time between one payment and another be one year or more. But if any payment be made before one year's interest hath accrued, then compute the interest on the principal sum due on the obligation for one year, add it to the principal; and compute the interest on the sum paid, from the time it was paid, up to the end of the year, add it to the sum paid, and dedoct that sum from the principal and interest, added as above. I any payments be made of a less sum than the interest arisen at the time of such payment, no interest is to be computed but only on the principal sum, for any period."

This Rule involves the same principles as Rule II. with the folJowing, viz.

That if an endorsement be made after a year's interest has accrued, but which is less than this interest, it shall not bear interest like the endorsements made before a year's interest has become due.

RULE IV.

The following Rule is established for the practice of the Courts in the State of New York.

The Rule for casting Interest, when partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest then due. If the payment exceeds the interest, the surplus goes towards discharging the principal, and the