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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.
EXAMPLES. 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, kec koning at 6 per cent. ? 1800.
dols. days. products. June 1, Principal per bill, 2000 | 79 158000 August 19, Received in part, 400
: Balance, 1600
91200 October 15, Received in part, 600 Balance, 1000
57000 December 11, Received in part, 400 1801. - Balance, 600
40800 February 17, Received in part, 200
Balance, 400 104 41600 June 1, Rec'd in full of principal, 400
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 endorse. ments, 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 yerir "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 tiine between one payment and another be one year or more. But if any payment be made before one year's interest bath accrued, then compute the interest on the principal sun due on the obligation for one year, add it to the principal, and compute the interest or. the sum paid, from the time it was paid, up to the end os the year: add it to the sum paid, and deduct that suin 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 coni puted 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. Ist 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 24t) of December, 1800 ? 1000,00 dated January 4, 1797.
67,50 interest to February 19, 1798=131 months. : 1067,50 amount.
(Carried up.] vt * If a year does not exterd beyond the time of final settlement; but isit 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 amouni from the amount of tne princina
1 067,50 amount.
200,00 first payment deducted.
867,50 balance due, Feb. 19, 1798.
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 duc on the Note, Dec. 24, 1800.
RULE II. į tablished by the Courts of Law in Massachusetts for Pomputing interest on notes, foc. on which partial paynents have been endorsed.
Compute the interest on the principal sum, from the lin ; when the interest commenced to the first time when a poyment was made, which exceeds either alone or in conjunction with the preceding payment (if any) the interest at that time duc: 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 ard subtract the payments as upon the first principal, and proceed in this manner to the time of final settlement.”
*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 1-2 months. 269,75 amount.
Let the foregoing example be solved by this Rule. A note for 1000 dols. dated Jan. 4, 1797, at 6 per eento 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 wer, 1800 ?
$ cts. Principal, January 4, 1797,
1000,00 Interest to February 19, 1798, (131 mo.) 67,50
Amount, 1067,50 Paid February 19, 1798,
Remainder for a new principal,
867,50: Interest to June 29, 1799, (16mo.)
Amount, 938,34, Paid June 29, 1799,
500,00 Remains for a new principal,
438,34 Interest to November 14, 1799, (41 mo.)
Amount, 448,24 November 14, 1799, paid .
260,00 Remains for a new principal,
188,20 Interest to December 24, 1800, (134 mo.) 12,70 Balance due on said note, Dec. 24, 1800, 200,90
$ cts. The balance by Rule I. 200,579
Rule II. 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 were payments andorsed upon it as follows, viz.
$cts. 1'st payment May 1, 1800,
40,00 2d payment November 14, 1800