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Case I. To find the present worth of a sum due some time hence. Rule.--As the amount of 100 dollars for the given time and rate, is to 100, so is the given sum to its present worth.
Examples. 1. What is the present worth 2. What is the present worth of 125 dollars, due 3 years hence, of 376 dolls. 20 cts. due at the discounting at the rate of 6 per end of 1 year and 6 months, discent? doll.
counting at 5 per cent? $100 Then 118:100 :: 125
Ans. $350. 18
3. A minister, settled with a 1800 Int. 118)12500(105.9325 salary of 300 dollars a year, 100
118 (Ans. wishing to build a house, his pa
--(pr't worth. I rishioners agreed to pay him 4. 118 Am't. 700
year's salary in advance, dis590
counting at 6 per cent. per an
num; how much ready money 1100
must they pay? 1062
Ans. $1047 04.
4. What is the present worth of €150, payable in 3 months, discounting at 5 per cent?
Ans. £148 2s. 112d.
Case II. To find the discount of any sum due some time hence. RulE.Find the present worth and subtract it from the given sum; or say, as the amount of 100 dollars for the given time and rate, is to the interest of 100 dollars for the given time and rate, so is the given sum to the discount required.
Examples. 1. What is the discount upon
2. What is the discount upon 125 dollars, due 3 years hence, 560 dollars due 9 months hence, per cent?
at 8 per cent ? Ans. $19.06747 discount.
Ans. 831.69**. 125 given sum. 105.932 present worth.
3. What is the discount of 50
dollars, due 2 years hence at 12 19.0674% discount, or 118:18::125
Ans. 89.677. QUESTIONS 1. What is Discount?
| 3. How is the present worth found? 2. What is the present worth of a 4. How is the discount found?
sum due some time hence?
4. Commission, Brokerage and knsurance.
1. COMMISSION is an allowance of so much per cent, to an agent abroad, for buying and selling goods for his employer.
2. BROKERAGE is an allowance of so much per cent. to a person called a Broker, for assisting merchants and others in procuring and disposing of their goods, &c.
3. INSURANCE is a premium of so much per cent. given to certain persons, or companies, for a security for making good the loss of ships, buildings, goods, &c. which may happen by fire, storms, &c.*
Rule. Commission, Brokerage and Insurance are calculated by the fir rule given for computing Simple Interest.
Examples. 1. What must I allow for sel 4. If [ allow my Broker 38 ling 525 dollars. worth of Goods, per cent. what must I allow him. at 3 per cent. commission ? for purchasing 2525 dolls. worth 525
of goods ? 3
Ans. $88 37 cts. 5 m.
per cent ?
5. What is the insurance of a 2. What comes the comimis- house, worth 3460 dollars, at
Ans. $17 30 cts. sion of 827 dolls. 64 cts. to, at 22 per cent ? Ans. 20 dolls. 69 cts. I m.
6. What is the insurance of
£1200, at 72 per cent? 3. What is the brokerage of
Ans. 90. 2610, at & per cent?
Ans. £1 10 s. 6 d.
1. What is Commission ?
4. What is the rule for computing
Commission, Brokerage, and Insurance ?
* Insurance is made by a writing called a policy, which should always be sufficient to cover the principal and premium; that is, a policy to secure the payment of 100 dollars, at 6 per cent. must be taken out for 106 dollars.
PRACTICE is a contraction of the Rule of Three when the first term is a unit. It took its name from its daily use among merchants. The necessity of this rule is nearly superceded by the use of Federal Money.
Rule. 1. Suppose the price of the given quantity to be £1, 1s. 1 d. or 1 qr. per pound, yard, &c. as is most convenient; then the quantity itself will be the answer at the supposed price.
2. Divide the given price into aliquot parts, either of the supposed price, or of one another, and the sum of the quotients belonging to each, will be the true answer required. PROOF.-By the Rule of Three.
Table of aliquot parts of Money. Parts of shill. of a pound. Parts of pound. | Parts of a pound. d.
10 0 4
8 0 3
5 0 2
Parts of a penny.
2 2 = 5
* Practice admits of a great number of cases. But as the rule is losing its importance, and going out of use in consequence of the introduction of Federal Money, it was thought best to introduce one general rule, and not perplex the scholar with a multiplicity of almost useless cases. This rule, with a little attention, will readily be applied to the solution of all questions which belong to it.
When there is a fractional part of a pound or yard, take an equal part of the price of one yard, that is, for one half, take half the price; for one fourth, take one fourth ; for three fourths, take three fourths of the price of one pound of yard.
Examples. 1. What will 225 yards cost, 10. What will 845 yards cost, at 2 qrs. per yard ?
at 8s. per yard? Ans. £338. 2)225d. the price at 1d. per yard,
11. What will 845 yards cost, 12)112 d. the price at 2 qrs. because
at 6s. 8d. per yard ?
Ans. £281. 9s. 42d. Ans.
12. What will 468 lb. cost, at 2. What will 1776 yards cost, 6d. per pound? Ans. €11 14s. at Sd. per yard ?
13. What will 5275 lb. cost, at Ans. £22 4s. 2d. per pound? 3. What will 263 yards cost,
Ans. £43 19s. 2d. at 3 qrs. per yard ?
14. What will 435 lb. cost, at Ans. 16s. 54d.
4 d. per pound? 4. What will 135 yards cost,
Ans. £8 3s. 1 d. at id. per yard ? Ans. 5s. 7 d.
15. What will 426 yards cost, 5. What will 937} yards cost, at 4s. 9d. per yard ? at €3 178. 8d. per yard ?
Ans. 101 3s. 6d. Ans. £3640 12s. 6d.
16. What will 204 yards cost, 6. What will 784 yards cost. at 1s. 1d. per yard ? at 4d. per yard ?
Ans. £11 1s. Ans. £ 13 1s. 4d. 7. What will 395 gallons cost,
17. What will 5687 yards cost at 4s. 6d. per gallon?
at 70. per yard ? Ans. £88 17s. 6d.
Ans. £16 11s. 5 d. 8. What will 426 lb. cost, at 4s. 6d. per pound?
18. What will 68 lb. cost, at 11d. per pound?
Ans. £ 15 6s. Ans. €19 10s. 6d. 9. What will 354yards cost,
19. What will 76 yards cost, at 1 qr. yard ?
at 2d. per yard ? Ans. 12. 8d. Ans. 75. 4d. 2£qrs.
1. What is Practice ?
as necessary as it was formerly?
4. For what reason
2. Care and Irett. TARE AND TRETT are practical for deducting certain allowances which are made by merchants and tradesmen in selling their goods by weight.
Gross weight is the whole weight of any sort of goods, together with the box, cas or bag, &c. that contains them.
Tare is an allowance to the buyer, for the weight of the box, cask,, or bag, &c. which contains the goods bought.
Trett is an allowance of 4 lb. in every 104 lb. for waste, dust, &c.
Net weight is what remains after the allowances are made.
Case I. When Tare is so much per box, cask, góc. RULE.-Multiply the number of boxes, &c. by the tare, subtract it from the gross, and the remainder wiil be the net weight.
Examples 1. In 5 hogsheads of sugar, 2. In 24i barrels of figs, each each weighing 8 cwt. 1 qr. 9 lb. 3 qrs. 19 lb. gross, tare 10 lb.
per gross, tare 24 lb. per hogshead; barrel, how many pounds net? how much net weight ?
3. What is the net weight of 5
14 hogsheads of tobacco, each 5
cwt. 2 qrs. 17 lb. gross, tare 100 41 2 17 gross.
Ib. per hogshead ? 1 0 8 tare.
Ans. 66 cwt. 2 qrs. 14 lb.
cut. RULE.--Divide the gross weight by the aliquot parts of a cwt. contained in the tare, and subtract the quotient from the gross,
the remainder is the net weight.
Examples. 1. What is the net weight of 2. In 25 barrels of figs, each 33 cwt. 2 qrs. 18 lb. gross, tare 2 cwt. I qr. gross, tare 8 lb. per 16 lb. per cwt. ?
cwt. how much net ? cwt. qr. Ib.
Ans. 52 cwt. O qrs. 26 lb. 16 lb.-4)33 2 18 gross.
4 3 64