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When interest is to be calculated on cash accounts, &c. where partial payments are made; multiply the several balances into the days they are at interest, then multiply the sum of these products by the rate on the dollar, and divide the last product by 365, and you will have the whole interest due on the account, &c.
Lent Peter Trusty, per bill on demand, dated 1st of June, 1800, 2000 dollars, of which I received back the 19th of August, 400 dollars ; on the 15th of October, 600 dollars ; on the 11th of December, 400 dollars ; on the 17th of February, 1801, 200 dollars ; and on the 1st of June 400 dollars; how much interest is due on the bill, reckoning at 6 per cent. ? 1800.
dols. days. products. June 1, Principal per bill, 2000 79 158000 August 19, Received in part, 400
Balance, 1600 57 91200 October 15, Received in part, 600
Balance, 400 104
388600 Then 388600 ,06 Ratio.
cts. m. 365)23316,00(63,879 Ans. = 63 87 9+ The following Rule for computing interest on any note, or obligation, when there are payments in part, or endorsements, was established by the Superior Court of the State of Connecticut, in 1784.
RULE. " 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 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 pay ments endorsed upon it as follows, viz. 1st payment February 19, 1798,
200 2d payment June 29, 1799,
500 3d payment November 14, 1999,
260 I demand how much remains due on said note the 24t? 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 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 the 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 principat.
70,845 interest to June 29, 1799=164 months
26,30 interest for one year.
mo. da. 5,687 interest to December 24, 1800.
5 25 200,579 balance due on the Note, Dec. 24, 1800.
Established by the Courts of Law in Massachusetts for
computing interest on notes, fc. on which partial payments have been endorsed.
“Compute the interest on the principal sum, from the lime 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 payments (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 settlemeent."
$ cts. *260,00 third payment with its interest 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 7 and 12 months 269,75 amokna.
Let the foregoing example be solved by this Rule. A note for 1000 dols. dated Jan. 4, 1797, at 6 per cept. 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 Decem ber, 1800 ?
* cts. Principal, January 4, 1797,
1000,00 Interest to February 19, 1798, (131 mo.)
Amount, 1067,50 Paid February 19, 1798,
200,00 Remainder for a new principal,
867,50 Interest to June 29, 1799, (16} mo.)
Amount, 938,34 Paid June 29, 1799,
500,00 Remains for a new principal,
438,34 Interest to November 14, 1799, (44 mo.)
Amount, 448,20 November 14, 1799, paid
260,00 Remains for a new.principal,
188,20 Interest to December 24, 1800, (13.mo.) 12,70 Balance due on said note, Dec. 24, 1800, 200,90
cts. The balance by Rule I. 200,579
Rule Il. 200,990
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 wote payments endorsed upon it as follows, viz.
$ cts. 1st payment May 1, 1800,
40,00 2d 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 September, 1801 ?
* cts. Principal dated February 1, 1800,
500,00 Interest to May 1, 1800, (3 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
50,00 New principal May 1, 1801,
445,55 Interest to Sept. 16, 1801, (4; mo.)
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 1, 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 befora