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DEFINITION.-Discount is a sum of money abated for the ready payment of money due at a future time.
RULE.-As the amount of 100 dollars for the Sime given is to 100 dollars ; so is the given sum, to its present worth : subtract the present worth from the given sum, the remainder is the discount.
Examples. 1. A. owes B. 1000 dollars payable in: one year; A. offers to pay the ready money if B. will make discount, -it 6 per cent. ; I demand the discount to be made.
dols. dols. dols. dols: As 106 : 100 :: 1000: 943-3976 present worth.
NOTE. It is thought by many, that the interest of she sum for the time, is the discount which ought to be nade ; but this is an error. I sliall here observe if B. aad discountert the interest of 1000 dollars for a year, the discount would have been 60 dollars; and he would have had but 940 dollars in ready money, which allow him to receive, and put at interest to a third person ; and at the end of a year he would receive but $996.40 cents for the 1000 dollars ; therefore he receives $3.60 less, than he would have received of A. had it remained in his hands; but allow B. to receive 943.39,6
189 cents of A. in ready money ; and put it at interest to D. in one year it would amount to just 1000 dollars ; Therefore by this rule neither party suffers any injury.
2. What discount must be made on 560 dollars due in 9 months ; discount at 8 per cent. per annum?
RULE II. As the amount of 100 dollars for the time and rate per cent. is to the interest of 100 dollars for the time and at the rate per cent so is the given sum to the dis. count to be made.
Examples. 1. What is the discount upon 1000 dollars due in a year ; at 6 per cent per annum?
dols. dols, dols, cts. As 106
1000 : 56.60, Ans. 2. What is the discount upon 560 dollars due 9 months hence ; at 8 per cent. per annum ?
Ans. $31.69 3. What is the discount upon 75 dollars due in 3 years ; at 3 per cent. per annum ?
8 6 107
EQUATION OF PAYMENTS. DEFINITION.-The use of this rule is to find a certain time to make a payment of several sums of money at once, due at several different times.
RULE.-Multiply each separate payment by the time when it would become due ; add the several products together for a dividend ; add the several separate pay. ments together for a divisor ; divide, and the quotient is the equated time.
Examples. 1. Ai owes B. 100 dollars payable in 9 months : 72 dollars payable in 6 months : and 200 dollars pay: able in 22 months : in what time
may A. pay
all the notes at once, that neither party shall not be liable to suffer any harm ? First payment 100 X 9 mo.
900 second do. 72 x 6 mo.
432 third do.
200 X 22 mo. 4400
-5732 dividend, 5732 - 372 - 15 mo. 1239 days Ans.
2. C. owes D. 100 dollars on demand ; 100 dolÍars in one year ; 100 dollars in two years ; 100 dol. last in there years; what is the equated time to pay all at once?
Ans. 1 year.
me cts y is
Definition.-Aligation medial is a rule made use of, to find the price of a compound of several things mixed together : the prices of the ingredients and quantities being known.
RULE.-As the sum of all the quantities, is to the total value of all the quantities, so is any part of the mixture to the price of that part.
Examples. 1. A farmer mixes 4 bu, of blighted corn at 42 cents per bu.; 6 bu, of oats at •33 cents; 5 bu. of barley at •96 cents; and 15 bu, of potatoes at :20 per bu. ; what is one bu. of the mixture worth?
bui. cis. D. cts. Corn
4 at 42 1.68 Oats
6 •33 = 1.98
5 .96 = 4.80
$11.46 :: 1 : 38 Ans. 2. A trader (mixes 60 gal. of rum at • 62 gal. at •80 cts. ; 40 gal. at •45 cts.'; and 10 gal. of water : what is 10 gal. worth?
Ans. $7.067 cts. 3. A trader mixes 1 cwt. of sugar at 10 dollars per cwt. with 3 cwt. at 12 dollars, and adds 40 lbs. ní sand to the mixture ; what is the value of 1 cwt. of the mixture?
DEFINITION.-Aligation alternate is a rule made use of to find the quantity of any number of simples, whose prices are given, that will make a mixture worth a certain price, therefore it is the reverse of aligation medial, and may be proved thereby.
Rule.Write down the prices of the several simples in a column, one above the other, beginning with the least, &c. on the left of the column draw a perpendicular line ; and on the left of the line, write down the price of the mixed quantity; then connect with a curved line each of the simples which is less, with one that is greater than the mixed quantity; and set the difference between the least simple and price of the mixed quantity) against the simple that is largest ; and the difference of the larger against that which is less, &c. after having connected each simple that is less with one that is greater, and found the differences ; the figures standing against each simple will express the quantity that must be taken of that price, to form a mix: ture of the price intended.
Examples. t. A farmer would make a mixture, of corn at •50 cents; oats at •25 cents; barley at •90 cents; and potatoes at .20 cents, per bush. : I demand the quantity of each that must be taken, that the mixturę may
be worth •30 cents per bushel.
20 cts. 259 30 50/
60 bushels of potatoes, will make a
30 cents per
NOTE.- Questions in this rule adınit of a great variety of ans swers, according to the manner of their being linked together; and yet the value of the mixture will be the same,
Proof by aligation medial.
•30 Ans. 2. A seller of wines would mix wine at •90 cts. .80 cts ; 70 cts, .60 cts. and .50 cts. per gallon; and take such a quantity of each, that the mixture may be worth •85 cts. per gallon : I demand the quantity of each that may be taken, This question admits of a variety of linkings.
5 at •70
5 at .80 35+25+15+5 80 at 90 90