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ment; 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 nade, 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 deduct that sum from the principal and interest added as above.*

1

"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.

2d payment June 29, 1799.

$ 200

500

260

3d payment November 14, 1799

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=13) months.

1067,50 amount.

[Carried up

*If a year does not extend beyond the time of final settlement; but if it does, then fiud the amount of the principal sum due on the obligation, up to the time of settlement, and likewise find the amount of the sum paid, from the time it was paid, up to the time of final settlement, and deduct this amount from the amount of the principal. But if there be several payments made within the said time, find the amount of the several payments, from the time they were paid, to the time of settlement, and deduct their amount from the amount of the principal,

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

867,50 balance due, Feb. 19, 1798.
70,845 interest to June 29, 1799-16 months.

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

[Brought

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 71⁄2 months.*

194,895 balance due June 29, 1800.

mo. da.

5,687 Interest to December 24, 1800. 5 25

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

Established by the Courts of Law in Massachusetts computing interest on notes, &c. on which partial p ments have been endorsed.

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

ment."

S.cts.

*260,00 third payment with its interest from the time 9,75 was paid, up to the end of the year, or fr Nov. 14, 1799 to June 29, 1800, which is 269,75 amount."

[months

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. 2d payment June 29, 1799.

$200

500

3d payment November 14, 1799.

260

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

cts.

Principal, January 4, 1797,
Interest to Feb. 19, 1798, (134 mo.)

Paid February 19, 1798,

Remainder for a new principal,
Interest to June 29, 1799, (16 mo.)

Amount, 1067,50

200,00

Amount,

Paid June 29, 1799,

Remains for a new principal,
Interest to November 14, 1799, (41 ma.)

Amount,

The balance by Rule I.
By Rule II.

November 14, 1799, paid

Remains a new principal,
Interest to December 24, 1800, (13) mo.)

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

cts. 200,579 200,990

1000,00
67,50

867,50

70,84

938,54

500,00

458,34

9,86

448,20

260,00

188,20

12,70

200,90

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.

1st payment May 1, 1800,

$ cts.
40,00

2d payment November 14, 1800,

8,00

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12,0

Sd payment April 1, 1801.
4th payment May 1, 1801.

$0,0

How much remains due on said note the 16th of 5 tember, 1801 ?

$ct 500,C 7,5

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Principal dated February 1, 1800,
Interest to May 1, 1800, (5 mo.)

Amount, 507,5

Paid May 1, 1800, a sum exceeding the interest, 40,0

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

Paid Nov. 4, 1800, a sum less than the
interest then due,

Paid April 1, 1801, do. do.
Paid May 1, 1801, a sum greater,

Amount, 495,5

New principal May 1, 1801,
Interest to Sept. 16, 1801, (41 mo.)

467,5

8,00

12,00 $0,00

28,0.

50,00

445,55 10,0%

Balance due on the note, Sept. 16, 1801,

$455,57

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

COMPOUND INTEREST BY DECIMALS.
RULE.

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

OR, In Table I. Appendix, find the amount of one do lar, or one pound, for the given number of years, whic multiply by the given principal, and it will give th amount as before.

EXAMPLES.

1. What will 400l. amount to in 4 per annum, compound interest ?

400×1,06×1,06×1,06×1,06=£504,99+ or

[£504 19s. 9d. 2,75qrs.+ Ans.
The same by Table I.
Tabular amount of £11,26247
Multiply by the principal

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

8

64

8

at 6 years, per

Whole amount=£504,98800 2. Required the amount of 425 dols. 75 cts. for 3 years, Ans. $507,7cts. + at 6 per cent. compound interest.

3. What is the compound interest of 555 dols. for 14 years, at 5 per cent.? By Table I. Ans. $543,86cts.+ 4. What will 50 dollars amount to in 20 years, at 6 per Ans. $160 35cts. 6m. cent, compound interest ?

512
8

INVOLUTION.

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

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

EXAMPLES

400

2d power, or square.

3d power, or cube.

cent.

4096 4th power, or biquadrate.

8

32768 5th power, or sursolid. Ans.

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