7. What is the interest on a note of $820 from April 16th, 1846, to Jan. 10th, 1847, at 6 per cent.?

8. What is the interest on a note of $615.44 from Oct. 1st, 1836, to June 13th, 1840, at 4 per cent.?

9. What is the interest on a note of $1830.63 from Aug. 16th, 1841, to June 19th, 1842, at 7 per cent. ?

10. What is the amount due on a note of $520 from Sept. 2d, 1846, to March 14th, 1847, at 5 per cent.?

11. What is the amount due on a note of $25000 from Aug. 17th, 1845, to Jan. 17th, 1846, at 7 per cent.?

12. What is the amount due on a note of $6200 from Feb. 3d, 1846, to Jan. 9th, 1847, at 6 per cent.?

PARTIAL PAYMENTS.

416. 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 New York, Massachusetts, and most of the other States of the Union. It is given in the language of the distinguished Chancellor Kent.-Johnson's Chancery Reports, Vol. I. p. 17.

QUEST.-416. What is the general method of casting interest on Notes and Bonds, when partial payments have been made?

$965.

NEW YORK, March 8th, 1843.

13. For value received, I promise to pay George B. Granniss, or order, Nine Hundred and Sixty-five Dollars, on demand, with interest at 7 per cent. HENRY BROWN.

The following payments were endorsed on this note:
Sept. 8th, 1843, received $75.30.

June 18th, 1844, received $20.38.

March 24th, 1845, received $80.

What was due on taking up the note, Feb. 9th, 1846 ?

Operation.

Principal,

$965.00

Interest to first payment, Sept. 8th. (6 months,)
Amount due on note Sept. 8th,

33.775

$998.775

75.30

$923.475

1st payment, (to be deducted from amount,) Balance due after 1st pay't., Sept. 8th, 1843, Interest on Balance to 2d pay't., June

18th, (9 mo. 10 d.,) 2d pay't., (being less than int. then due,) Surplus int. unpaid June 18th, 1844, Int. continued on Bal. from June 18th, to March 24th, 1845, (9 mo. 6 d.,)

Amount due March 24th, 1845,

} $50.278

20.38
$29.898

}

49.559

79.457

$1002.932

80.00

$922.932

56.529

$979.461

3d pay't., (being greater than the int. now due,)

is to be deducted from the amount,

Balance due March 24th, 1845,

Int. on Bal. to Feb. 9th, (10 mo. 15 d.,)

Bal. due on taking up the note, Feb. 9th, 1846,

$650.

BOSTON, Jan. 1st, 1842.

14. For value received, I promise to pay John Lincoln, or order, Six Hundred and Fifty Dollars on demand, with interest at 6 per cent. GEORGE LEWIS.

Endorsed, Aug. 13th, 1842, $100.

Endorsed, April 13th, 1843, $120.

What was due on the note, Jan. 20th, 1844?

$2460.

PHILADELPHIA, April 10th, 1844.

15. Four months after date, I promise to pay James Buchanan, or order, Two Thousand Four Hundred and Sixty Dollars, with interest, at 6 per cent., value received.

16. Six months after date, I promise to pay John Fairfield, or order, Five Thousand Dollars, with interest at 5 per cent., value received. WILLIAM ADAMS.

Sept. 13th, 1846, $480.

What was the balance due Jan. 1st, 1847 ?

CONNECTICUT RULE.

417. I. "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."

II. "If any payments be made before one year's interest has 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."

III. "If a year extends beyond the time of payment, 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."

"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.

THIRD RULE.

418. First find the amount of the given principal for the whole time; then find the amount of each payment from the time it was 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.

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

419. To compute Interest on Sterling Money.

17. What is the interest of £241, 10s. 6d. for 1 year, at 6 per cent.?

Operation.

£241.525 Prin.

.06 Rate.

£14.49150 Int. 1 yr.
20s.=£1.

s. 9.83000

*12d.=1s.

d. 9.96000

4f.=1d.

far. 3.84000

Ans. £14, 9s. 9 d.

We first reduce the 10s. 6d. to the decimal of a pound, (Art. 346,) then, multiply the principal by the rate, and point off the product as in Art. 404. The 14 on the left of the decimal point, denotes pounds; the fig ures on the right are decimals of a pound, and must be reduced to shillings, pence, and farthings. (Art. 348.} Hence,

419. a. To compute the interest on pounds, shillings, pence, and farthings.

Reduce the given shillings, pence, and farthings to the decimal of a pound; (Art. 346;) then find the interest as on dollars and cents; finally, reduce the decimal figures in the answer to shillings, pence, and farthings. (Art. 348.)

18. What is the amount of £156, 15s. for 1 year and 4 months, at 5 per cent.? Ans. £167, 4s. 19. What is the int. of £275, 12s. 6d. for 1 yr., at 7 per cent.? 20. What is the int. of £89, 7s. 61d. for 2 yrs., at 5 per cent.? 21. What is the int. of £500 for 6 mo., at 5 per cent.? 22. What is the amt. of £1825, 10s. for 8 mo., at 6 per cent.? 23. What is the amt. of £2000 for 10 yrs., at 4 per cent.?

QUEST.-419. a. How is interest computed on pounds, shillings, and pence ?

PROBLEMS IN INTEREST.

420. 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 questions, therefore, which may arise in interest, are numerous; but they may be reduced to a few general principles, or Problems.

OBS. A number or quantity is said to be given, when its value is stated, or may be easily inferred from the conditions of the question 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.

PROBLEM I.

421. To find the INTEREST, the principal, rate per cent., and the time being given.

This problem embraces all the preceding examples pertaining to Interest, and has already been illustrated.

PROBLEM II.

To find the RATE PER CENT., the principal, the interest, and the time being given.

Ex. 1. A man borrowed $80 for 5 years, and paid $36 for the use of it: what was the rate per cent.?

Analysis.-The interest of $80 at 1 per cent. for 1 year is 80 cents; (Art. 404;) consequently for 5 years it is 5 times as much, and $.80×5=$4. Now since $4 is 1 per cent. on the principal for the given time, $36 must be 36 of 1 per cent., which is equal to 9 per cent. (Art. 196.)

Or, we may reason thus: Since $4 is 1 per cent. on the principal for the given time, $36 must be as many per cent, as $4 is contained times in $36; and $36÷$49. Ans. 9 per cent.

QUEST-420. How many terms are connected with each of the preceding examples? What are they? When three are given, can the fourth be found? Obs. When is a number or quantity said to be given?