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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.*
"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.
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.
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.
*If a year does not extend beyond the time of final settlement; 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 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.
200,00 first payment deducted.
867,50 balance due, Feb. 19, 1798.
70,845 interest to June 29, 1799-163 months.
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 7 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, 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 settle
*260,00 third payment with its interest from the time it was paid, up to the end of the year, orfrom Nov. 14, 1799 to June 29, 1800, which is 7 269,75 amount."
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.
3d payment November 14, 1799.
How much remains due on said note the 24th of De
cember, 1800 ?
Principal, January 4, 1797,
Interest to Feb. 19, 1798, (133 mo.)
Remains for a new principal,
Interest to November 14, 1799, (4) ma.)
November 14, 1799, paid
Remains a new principal,
Interest to December 24, 1800, (13) mo.)
Balance due on said note, Dec. 24, 1800,
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 pay
ments endorsed upon it as follows, viz.
1st payment May 1, 1800,
2d payment November 14, 1800,
$d payment April 1, 1801.
4th payment May 1, 1801.
How much remains due on said note the 16th of Sep
tember, 1801 ?
Principal dated February 1, 1800,
Interest to May 1, 1800, (3 mo.)
$ cts. 500,00
Paid May 1, 1800, a sum exceeding the interest, 40,00
interest then due,
New principal, May 1, 1800,
Interest to May 1, 1801, (1 year.)
Paid Nov. 4, 1800, a sum less than the
Paid April 1, 1801, do.
Paid May 1, 1801, a sum greater,
New principal May 1, 1801,
Interest to Sept. 16, 1801, (4) mo.)
Balance due on the note, Sept. 16, 1801,
The payments being applied according to this Bule, keep down the interest, and no part of the interest ever forms a part of the principal carrying interest.
COMPOUND INTEREST BY DECIMALS.
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.
1. What will 400l. amount to in 4 years, at 6 per cent.
per annum, compound interest ?
400×1,06×1,06 × 1,06×1,06 £504,99+ or
[504 19s. 9d. 2,75grs.+ Ans.
The same by Table I.
Tabular amount of £1,26247
Multiply by the principal
2. Required the amount of 425 dols. 75 cts. for 3 years, at 6 per cent. compound interest. Ans. $507,7 cts. + 3. What is the compound interest of 555 dols. for 14 years, at 5 per cent. By Table I. Ans. $545,86cts.+ 4. What will 50 dollars amount to in 20 years, at 6 per cent, compound interest? Ans. $160 35cts. 6m.
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.