1853, received $130.
15, 1853, received $300.

July 20, 1853, received $400. Sept.
What is due Jan. 4, 1854.

Ans. $274,97.

WINDHAM, Feb. 6, 1853.

For value received, I promise to pay Amos Hanson, or order, eight hundred and forty dollars, on demand, with interest. $840. MARK KNIght. Endorsements.-May 16, 1853, received $180. July 8, 1853, received $100. Aug. 19, 1853, received $60. Oct. 14, 1853, received $250. What was due Dec. 12, 1853?

Ans. $280,54.

515. Though the preceding is, by some, considered the only equitable rule, the following is the legal one, as stated in the N. Y. Chancery Reports, (see Emerson's Third Part, page 104 :)

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

NEW YORK, July 8, 1850.

For value received, I promise to pay Hyacinthe Peugnet, or order, one thousand five hundred dollars, on demand, with interest. JEAN MANESCA.

$1500.

Endorsements.-Nov. 19, 1851, received $200. Oct. 16, 1852, received $50. July 11, 1853, received $45. Oct. 20, 1853, received $560. What was due Dec. 12, 1853?

Principal......$1500,00 Int. from July 8, 1850, to Nov. 19, 1851, (1 yr.

4 mo. 11 d.,)....

122,75

Amount...... 1622,75

First pay't exceeding int....... 200,00

New principal...... 1422,75

Int. from Nov. 19, 1851, to Oct. 16, 1852,

(10 mo. 28 d.,).

.877,78 Sec'd pay't less than int....... 50,00 Balance of int. due...... 27,78 Int. from Oct. 16, 1852, to July 11, 1853,

(8 mo. 25 d.,)..

62,85

90,63

Third pay't less than int....... 45,00
Balance of int. due...... 45,63
Int. from July 11, 1853, to Oct. 20, 1853,
(3 mo. 9 d.,)...

23,47 $69,10

Amount due Oct. 20, 1853. 1491,85 Fourth pay't exceeding int....... 560,00

Int. from Oct. 20, 1853, to Dec. 12, 1853,

(1 mo. 22 d.,)..................

New principal......

931,85

8,07

..$939,92

Amount due Dec. 12, 1853.....

WESTBROOK, Feb. 20, 1850. For value received, I promise to pay Jeffery Smedley, or order, one thousand dollars, on demand, with interest. *

$1000.

NOBLE HEATH, JR.

-Oct. 15, 1850, received $150. Nov. 3,
Aug. 26, 1852, received $40. Jan. 5,
June 9, 1853, received $300.

Endorsements. 1851, received $50. 1853, received $45. 1853, received $400.

11, 1854?

Sept. 29,

How much was due on this Note, Mar.
Ans. $212,07.

Discount.

516. This is an allowance of so much p. c. for the payment of money before it is due, or for prompt payment in the purchase of goods on which credit is allowed. The latter is sometimes called Rebate.

As $100 at 6 p. c. amounts, in one year, to $106, it is plain that $100 is the present worth of $106, payable at the end of .that time. Hence the ratio of any sum, due at the end of one year at 6 p. c., to its present worth, is 106 1,06; wherefore (219) any sum multiplied by 1.6, which is the reciprocal of this ratio; that is, divided by 1,06, will give its present worth for one year at 6

p. c.

00

Ex. 1. If A has B's Note for $583, due in one year, without

int., how much should A allow B for prompt payment, discount at 6 p. c.?

$583 $550 present worth; then

1,06

583550: =

$33 discount, which A allows B. Proof. 550,06 $33 int. and $550+ 33583 Am't of Note.

=

517. As 188 is the ratio of any sum due at the end of one year to its present worth; and the rate 6 p. c., the discount of 106, which will give the present worth, it is plain that 1066 any sum: its discount at 6 p. c.

Hence the rule: Multiply any given sum by the rate p. c. and divide by 100 plus that rate.

2. Thus for the discount of the above note, we say,

8. £967 16 s. 11 d. at 7 p. c.

£7 6s. 63 d.+87 qr. ...£63 6 s. 4787 2 d.

9. £1056 17 s. 113 d. at 8 p. c.......£78 5 s. 91 d. 27 qr. Required the present worth of each of the following sums: 10. $100 at 7 p. c....... Ans. $93,46 11. $546,50 at 8 p. c. Prove as in Ex. 1....... $506,0133. 12. £967 16 s. 11 d. at 7 p. c.. .£904 10 s. 6.98 d.

107

13. £1056 17 s. 112 d. at 8 p. c.....£978 12 s. 24 d. 30 qr.

518. Though the preceding is undoubtedly the equitable or true rule of Discount, it is by no means that which is generally practiced. The Bank Rule is to deduct the interest of the given sum for the given rate and time.

Thus, if, where the int. is 6 p. c., we present a Note of $500 for discount, the Bank deducts $30, which is the int. of $500 for one year at 6 p. c. and we receive $470 for the Note. This, therefore, needs no further elucidation.

By the true rule, the present worth is the sum which, at int. at the given rate, will reach the amount of the Note. But we find that the int. of $470 at 6 p. c. is only $28,20, and the amount $498,20, instead of $500.

519. The amount of discount being given, to find the true

rate. Let q

the rate; D, the discount; P, the present worth, and S, the amount of Note. Then by the true rule, (517,) 100 g:q: S: D dividendo, (410.)

100 : q

::P: D alternando, (408.)

100 Pg: D invertendo, (408.)

P: 100 Dq; that is,

The present worth is to 100, as the given discount to the rate. Ex. 1. Having, for a Note of $500, received $470; what is the true rate of discount?

470 100:30: 618 p. c. the required rate.

Proof. $4,7061,1 × 300 = $30.

520. The Bank rate, being merely the int., is found thus: 5100 100:30: 6 p. c.

Hence, we have the following rule:

For the true rate, divide 100 times the discount by the present worth. For the Bank rate, divide 100 times the disc. (or rather int.) by the whole sum.

2. Having at a bank received $558 for a Note of $600, what is the true, as well as the Bank, rate of discount? Ans. True rate 743 p. c.; Bank rate, 7 p. c.

Prove thus: 5,58 × 749 =,06 X 700

Also, 6,00 × 7 = 42.

=

= 6 X 7

= 42.

3. Having discounted a Note of $720, for which was received $662,40, what is the rate p. c.? True rate, 819 p. c.; Bank rate, 8 4. Having for a Note of £575 5 s., received £546 9 s. 9 d., what is the rate of discount?

True rate, 55 p. c.;

Insurance.

p. c.

Bank rate, 5 p. C.

521. This is a bond or contract between two parties by which one engages, for a certain sum, to indemnify the other for loss sustained in his property, which is liable to damage by fire, by the perils of the seas, or otherwise; and is effected on houses or other buildings, ships, goods, &c.

The party who assumes the risk is called the insurer, assurer, or underwriter, and the owner of the property, the insured or assured.

The sum paid for insurance, which is a percentage on the property insured, is called the premium, and the instrument containing the contract is called the policy.

Ex. 1. At 51 cts. per $100, what is the premium on $6275? Ans. $32,001.

2. Effected insurance of £5000 on the ship Noble Ann, of So. Shields, on a voyage to Buenos Ayres, out and home; what did the premium amount to at 2 p. c.?

Ans. £125. 3. A farmer insures his house for $1000, at a premium of 11 p. c.; his barn for $3200, at a premium of 13 p. c., and his other out-buildings for $500, at a premium of 2 p. c. does he pay on the whole? Ans. $72,25.

Duties.

What

522. These are imposts levied by government, at an establishment called the Custom-House, on certain kinds of goods imported into a country. On the re-exportation of some goods, an allowance is restored to the exporter, called the drawback.

The whole weight of goods, as imported in casks, bags, boxes, chests, &c., is called gross weight.

From this weight is first deducted a small allowance for waste, called DRAFT, which is as follows:

On a single package, weighing 1 cwt., (112 lb.) ... 1 lb. above 1 cwt. and under 2 cwt.

66 2

2

523. This is an allowance made, subsequently to draft, for the bag, box, chest, &c. containing the goods; and in computing it on the remainder, less than lb. is not reckoned; more is called 1 lb.

For leakage and breakage 2 p. c. is allowed on the gauge of all merchandise in casks paying duty by the gallon; 10 p. c. on beer, ale, and porter, in bottles, and 5 p. c. on all other bottled liquors. There are other commercial allowances which are not recognised at the Custom-House.

After the deduction of all allowances, the remainder, or real weight of the goods, on which duty is computed, is called net weight.

1. What is the duty on 4 boxes of sugar, weighing gross, as follows: 1st. 6 cwt. 1 qr.; 2d. 6 cwt. 3 qrs.; 3d. 7 cwt. qr. 14 lb.; 4th, 7 cwt. 2 qrs. 10 lb.; draft as per table, tare 15 p. c.; the duty being 13 cts. per lb. ? Ans. $46,36.

1