PARTIAL PAYMENTS.

248. When partial payments are made and endorsed upon Notes and Bonds, the rule for computing the interest adopted by the Supreme Court of the United States, is the following.

I. "The rule for casting interest, when partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest then due.

II. If the payment exceeds the interest, the surplus goes towards discharging the principal, and the subsequent interest is to be computed on the balance of principal remaining due.

III. If the payment be less than the interest, the surplus of interest must not be taken to augment the principal; but interest continues on the former principal until the period when the payments, taken together, exceed the interest due, and then the surplus is to be applied towards discharging the principal; and interest is to be computed on the balance, as aforesaid."

Note. The above rule is adopted by Massachusetts, New York, and the other States of the Union, with but few exceptions. It is given in the language of the distinguished Chancellor Kent.—Johnson's Chancery Reports, Vol. I. p. 17.

$850.

NEW HAVEN, Jan. 1st, 1841.

43. For value received, I promise to pay George Howland, or order, eight hundred and fifty dollars, on demand, with interest at 6 per cent.

JOHN HAMILTON.

The following payments were endorsed on this note :

July 1st, 1841, received $100.62.
Dec. 1st, 1841, received $15.28.
Aug. 13th, 1842, received $175.75.

What was due on taking up the note, Jan. 1st, 1843?

QUEST. 248. What is the general method of casting interest on Notes and Bonds, when partial payments have been made?

Principal,

Operation.

Interest to first payment, July 1st, (6 months,)
Amount due on note July 1st,

1st payment, (to be deducted from amount,)
Balance due July 1st,

Int. on Bal. to 2d pay't Dec. 1st, (5 mo.,) $19.37

$850.00

25.50

$875.50.

100.62

$774.88

32.54

36.63

$811.51

Int. continued on Bal. from Dec. 1st,}

1842, to Aug. 13th, (8 mo. 12 d.,)

Amount due Aug. 13th,

3d payment (being greater than the interest

now due) is to be deducted from the am't.

Balance due Aug. 13th,

Int. on Bal. to Jan. 1st, (4 mo. 18 d.,)

175.75

$635.76

14.62

Balance due on taking up the note, Jan. 1. 1843, $650.38

$500.

NEW YORK, May 10th, 1842.

44. For value received, I promise to pay James Monroe, or order, five hundred dollars on demand, with interest at 7 per cent.

HENRY SMITH.

The following sums were endorsed upon it:

Received, Nov. 10th, 1842, $75.

Received, March 22d, 1843, $100.

What was due on taking up the note, Sept. 28th, 1843?

$692.35.

BOSTON, Aug. 15th, 1843.

John

45. Three months after date, I promise to pay Warren, or order, six hundred and ninety-two dollars and thirty-five cents, with interest at 6 per cent., value received. SAMUEL JOHNSON.

Endorsed, Nov. 15th, 1845, $250.375.

46. Six months after date, I promise to pay Messrs. Carey, Hart & Co., or order, one thousand dollars, with interest at 5 per cent., value received.

HORACE PRESTON.

Endorsed, Jan. 10th, 1844, $125.

66

June 16th, 1844, $93.

Feb. 20th, 1845, $200.

What was the balance due Aug. 1st, 1845?

CONNECTICUT RULE.

ART. 249. "Compute the interest on the principal 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 payments 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.

VERMONT RULE.

249.a. First find the amount of the given principal for the whole time; then find the amount of the several payments from the time they were endorsed to the time of settlement. Finally, subtract the amount of the several payments from the amount of the principal, and the remainder will be the sum due.

* If a year does not extend beyond the time of payment; but if it does, then find the amount of the principal remaining unpaid, up to the time of settlement, likewise the amount of the endorsements from the time they were paid to the time of settlement, and deduct the sum of these several amounts from the amount of the principal.

Note. It will be an excellent exercise for the pupil to cast the interest on each of the preceding notes by each of the above rules.

47. What is the interest of £175, 10s. 6d. for 1 year, at 5 per cent.?

Operation.

£175.525 Prin.

.05 Rate.

We first reduce the 10s. 6d. to the decimal of a pound, (Art. 200,) then multiply the principal by the rate and point

£8.77625 Int. for 1 yr. off the product as in Art. 241.

20

s. 15.52500

12

d. 6.30000

4

far. 1.20000

Ans. £8, 15s. 6d.

The figure 8 on the left of the decimal point is pounds, and those on the right are decimals of a pound, and must be reduced to shillings, pence, and farthings. (Art. 201.) Hence,

250. To compute the interest on pounds, shillings, &c. Reduce the given shillings, pence, and farthings, to the decimal of a pound; (Art 200;) then find the interest as in Federal Money; finally, reduce the decimal figures in the answer to shillings, pence, and farthings. (Art. 201.)

48. What is the interest of £56, 15s. for one year and 6 months, at 6 per cent.? Ans. £5, 2s. 14d.

49. What is the interest of £75, 12s. 6d. for 1 year and 3 months, at 7 per cent.?

50. What is the interest of £96, 18s. for 2 years and 6 months, at 4 per cent.?

51. What is the amount of £100 for 2 years and 4 months, at 5 per cent.?

52. What is the amount of £430, 16s. 10d. for 1 and 5 months, at 6 per cent.?

year

QUEST.-250. How is interest computed on pounds, shillings, &c.?

PROBLEMS IN INTEREST.

251. It will be observed that there are four parts or terms connected with each of the preceding operations, viz: the principal, the rate per cent., the time, and the interest, or the amount. These parts or terms have such a relation to each other, that if any three of them are given, the other may be found. The processes of finding the fourth from the three given parts are usually denominated Problems.

ОвS. 1. A Problem is a question proposed which requires a solu

tion.

2. A number or quantity is said to be given, when its value is stated or may be easily inferred from the conditions of the problem under consideration. Thus when the principal and interest are known, the amount may be said to be given, because it is merely the sum of the principal and interest. So if the principal and the amount are known, the interest may be said to be given, because it is the difference between the amount and the principal.

252. To find the interest on any given sum, as in the foregoing examples, the principal, the rate per cent., and the time are always given. This process constitutes the First and most important Problem in interest. The other Problems will now be illustrated.

PROBLEM II.*

1. A man loaned $75 to one of his neighbors for 4 years, and received $24 interest: what was the rate per

cent.?

Note. In this example it will be observed that the principal, the interest, and the time, are given, to find the rate per cent.

QUEST.-251. How many terms are connected with the preceding examples? What are they? Are they all given? When three are given, can the fourth be found? What is the process of finding the fourth term usually called? Obs. What is a problem? When is a number or quantity said to be given? 252. What terms are given when it is required to find the interest?

*Should this and the following Problems be deemed too difficult for beginners, they can be omitted till review.