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But if any

ment; it that be one year or more from the time the in terest commenced, add it to the principal, and deduct the payment from the sem total. If there be after payments inade, 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. payment be made before one year's interest hath accrued, then compute the interest on the principal sum due on the obligations for one year, add it to the principal, and compute the interest on the sum paid, froin the time it was paid, up to the end of the year: add it to the sum paid, and deduct that sum from the principal and interest added as above. *

If 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.”

Kirby's Reports, page 49.

EXAMPLES.

A bond, or note, dated January 4th, 1797, was given for 1000 dollars, interest at 6 per cent. and there were payments endorsed upon it as follows, viz. 1st payment February 19, 1798.

200 2d payment June 29, 1799.

500 3d payment November 14, 1799.

260 I demand how much remains due on said note the 24th of December, 1800 ? 1000,00 dated January 4, 1797.

67,50 Interest to February 19, 1798=134 months.

1067,50 amount.

[Carried up

* It a year does not extend beyond the time of final settlement; but if it does, then find the amount of the principal sum duc on the obligation, up to the time of settiennent, and likewise find the amount of the sum paid, from the time it was paid, up to the time of final settirment, and deduct this amount from the amount of the principai. But if there be several payments made within the said time, find the amount of the severai payments, from the line they were paid, to the time of settlement, and deduci their amount from the nnount of the principal,

[Brought up.

1067,50 amount.,
200,00 first payment deducted.

867,50 balance due, Feb. 19, 1798.
70,845 interest to June 29, 1799=164 months.

938,345 amount.
500,000 second payment deducted.

438,345 balance due, June 29, 1799. 26,30

interest for one year.

464,645 amount for one year.
269,750 amount of third payment for 74 months. *

mo. da

194,895 balance due June 29, 1800.

5,697 interest to December 24, 1800,

5 25

200,579 balance due on the Note, Dec. 24, 1800.

RULE II.

Established by the Courts of Law in Massachusetts for

computing interest on notes, &c. on which partial payments have been endorsed.

" Compute the interest on the principal sum, from the time when the interest commenced to the first time when a payment was made, which exceeds either alone or in conjunction with the preceding payment (if any) the interest at that time due : add that interest to the principal, and from the sum subtract the payment made at that time, together with the preceding payment (if any) and the remainder forms a new principal; on which compute and subtract the payments as upon the first principal, and proceed in this manner to the time of final settlement"

$ cis. *260,00 third payment with its interests from the time it was paid up to 9,75 the end of the year, or from Nov. 14, 1799 to June 29, 1800, which

is 74 months 269,75 amount.

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Let the foregoing example be solved by this Rule. A note for 1000 dols. dated Jan. 4, 1797, at 6 per cent. 1st payment February 19, 1798.

$200 2d payment June 29, 1799.

500 3d payment November 14, 1799.

260 How much remains due on said note the 24th of December, 1800 ?

$ cis. Principal, January 4, 1797,

1000,00 Interest to Feb. 19, 1798, (13}mo.) 67,50

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Remains for a new principal,
Interest to November 14, 1799 (4 mo.)

438,44

9,86

Amount, 448,20

260,00

November, 14, 1799, paid

Remains a new principal,

188,20 Interest to December 24, 1800, (134mo.) 12,70

Balance due on said note, Dec. 24, 1800, 200,90

$ cts. The balance by Rute 1. 200,579

By Rule' II. 200,990.

Difference, 0,411

Another Example in Rule II. A bond or note, dated February 1, 1800, was given for 500 dollars, interest at 6 per cent. and there were payments endorsed upon it as follows, viz. $ cts. 1st payment May 1, 1800,

40,00 3d payment November 33 1800,

8,00

3d payment April 1, 1801

12,00 1th payment May 1, 1801.

20,00 How much remains due on said note the 16th of Sep. tember, 1801 ?

$ cts. Principal dated February 1, 1800, 500,00 Interest to May 1, 1800, (3 mo.)

7,50

Amount, 507,50 Paid May 1, 1800, a sum exceeding the interest 40,00

New principal, May 1, 1800,
Interest to May 1, 1801 (1 year.)

467,50 28,05

Amount, 495,55 Paid Nov. 4, 1800, a sum less than the

interest then due, 8,00 Paid April 1, 1801, do. do. 12,00 Paid May 1, 1801, a sum greater, 30,00

50,00

New principal May 1, 1801,

445,55 Interest to Sept. 16, 1801, (41mo.)

10,02 Balance due on the note, Sept. 16, 1801, 455,57

The payments being applied according to this Rule, keep down the interest, and no part of the interest ever forms a part of the principal carrying interest.

COMPOUND INTEREST BY DECIMALS,

RULE. MULTIPLY the given principal continually by the amount of one pound, or one dollar, for one year, at the rate per cent. given, until the number of multiplications are equal to the given number of years, and the product will be the amount required.

Or, In Table I. Appendix, find the amount of one dollar, or one pound, for the given number of years, which multiply by the given principal, and it will give the amount as before,

EXAMPLES. 1. What will 4001. amount to in 4 years, at six per cent. per annum, compound interest ? 400 X 1,06x1,06 X 1,06 X 1,06=£504,99 for

[£504 198. 9d. 2,75qrs.+Ans.
The same by Table I.
Tabular amount of £1=1,26247
Multiply by the principal 400

Whole amount=£504,98800 2. Required the amount of 425 dols. 75 cts. for 3 years at 6 per cent. compound interest.

Ans. $507,7cts.+ 3. What is the compound interest of 555 duls, for 14 years, at 5 per cent. ? By Table I.

Ans. $543,86cts. + 4. What will 50 dols. amount to in 20 years, at 6 per cent. compound interest ? Ans. $160 35cts. 6.

INVOLUTION, Is the multiplying any number with itself, and that product by the former multiplier; and so on ; and the sereral products which arise are called powers.

The number denoting the height of the power, is called the index or exponent of that power:

EXAMPLES.
What is the 5th power of 8%
8 the root or 1st power.
8

64 =2d power, or squaro.
8

512 3d power, or cabe.

8

4096 4th power, or biquadrato.

8

32788-Oth

power, or sursolid. Ana

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