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if that be one year or more from the time the in terest 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 alsorbed ; 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.*
“ If any payments be made of a less sum than the in. terest arisen at the time of such payment, no interest in to be computed but only on the principal sum for any period."
Kirby's Reports, page 49. 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.
*If a year does not extend beyond the time of final setúement; but if it does, then find 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 severai payments made within the said time, find the amount of the several pay. ments, from the time they were paid, to the time of scttlenzent, and deduct their amount from the amount of the principal
867,50 balance due, Feb. 19, 1798.
438,345 balance due, June 29, 1799.
464,645 amount for one year..
194,895 balance due June 29, 1800.
5,687 interest to December 24, 1800,
200,579 balance due on the Note, Dec. 24, 1800.
Established by the Courts of Law in Mussachusetts 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 aud subtract the payments as upon the first principal, and proceed in this manner to the time of final settlement
*280,00 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, whicks
is 7 months: 369,75 amount.
Let the foregoing example be solved by this Rute. A note for 1000 dols.,dated Jan. 4, 1797, at 6
per cente 1st payment February 19, 1798.
$200 2d payınent June 29, 1799.
500 3d payment November 14,. 1799.
260 How much remains due on said note the 24th of Dea cember, 1800 ?
8 cts, Principal, January 4, 1797,
1000,00 Interest to Feb. 19, 1798, (13) mo.)
Amount, 1067,50 Paid February 19, 1798,
200,00 Remainder for a new principal,
867,50 Interest to June 29, 1799, (16] mo.)
Paid June 29, 1799,
Remains for a new principal,
November 14, 1799, paid
Remains a new principal,
Balance due on said note, Dec. 24, 1800,
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.
Scts. 1st payment May 1, 1800,
40,00 and payment November 14, 1800,
3d payment April 1, 1801.
12,00 4th payment May 1, 1801.
30,00 How much remains due on said note the 16th of Sepp tember, 18017
$ cts. Principal dated February 1, 1800,
500,00 Interest to May 1, 1800, (s mo.)
Amount, 507,50 Paid May 1, 1800, a sum exceeding the interest, 40,00
New principal, May 1, 1800,
467,50 Interest to May 1,1801, (1 year.)
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
New principal May 1, 1801,
445,55 Interest to Sept. 16, 1801, (41 mo.)
10,02 Balance due on the note, Sept. 16, 1801, 8455,57
p 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.
RUI.E. 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 dol. lar, or one pound, for the given number of years, which multiply by the given principal, and it will give the amount as before.
KXAMPLES. 1. What will 4001. amount to in 4 years, at 6 per cente per annum, compound interest ?
400X1,06x1,06x1,06 x 1,06=£504,99+ or
[£504 19s. 9d. 2,75qrs. + Ans.
Whole amount=$504,98800 2. Required the amount of 425 dols. 75 cts. for 3 years, at 6 per cent. compound interest. Ans. $507,7 icts. +
S. What is the compound interest of 555 dols. for 14 years, at 5 per cent. ? By Table I. Ans. $543,86cts. for
4. What will 50 dollars amount to in 20 years, at 6 per cent, compound interest ? Ans. $160 35cts. 6fm,
INVOLUTION. Is the multiplying any number with itself, and that praduct 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.
32768 = 5th power, or sursolid. Ano.