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EXAMPLES. 1 If an annuity of 701. be forborne 5 years, what will be due for the principal and interest at the end of said term, simple interest being computed at 5 per cent. per annum ?
Yr. £. 1st. Interest of 701. at 5 per cent. for 1-3 10
2 7 0 3-10 10
4-14 0 2d. And 5 yrs. annuity, at 70l. per yr. is 350 0
Ans. £385 0 2. A house being let upon a lease of 7 years, at 400 dollars per annum, and the rent being in arrear for the whole term, I demand the sum due at the end of the term, simple interest being alloved at Gl. per cent. per annum?
To find the present worth of an annuity at simple
interest. RULE.. Find the present worth of each year by itself, discounting from the time it falls due, and the suni of all these present worths will be the present worth required.
1. What is the present worth of 400 dols. per annum, to continue 4 years, at 6 per cent. per annum? 106
377,35849 Pres. worth of 1st yr. 112
357,14285 : 100 :: 400: 118
2d yr. 3d yr. 4th yr.
Ans. $1396,06503 – $139, Octs. 5m. 2. How much present money is equivalent to an annuity of 100 dollars, to continue 3 years; rebate being made at 6 per cent. ?
Ans. $268, 37 lei 3. What is 801. yearly rent, to continue 5 yaum ve in ready manney, at 6l. per cent. ?
EQUATION OF PAYMENTS, IS finding the equated time to pay at once, several debts due at different periods of time, so that no loss shall be
In sustained by either party.
dok RULE.—Multiply each payment by its time, and divide the sum of 001) the several products by the whole debt, and the quotient will be the equated time for the payment of the whole.
Pire EXAMPLES. 1. A owes B 380 dollars, to be paid as follows-viz. 100
3. dollars in 6 months, 120 dollars in 7 months, and 160 dollars in 10 months: What is the equated time for the pa ment of the whole debt?
4 100 x 6 600
I bart 120 X ny 840 160 X 10 1600
)3040(8 months. Ans. LE 2. A merchant hath owing him 3001. to be paid as fol lows : 501. at 2 months, 1001. at 5 months, and the rest al 8 months; and it is agreed to make one payment of the whole: I demand the equated time? Ans. 6 months.
3. F owes H 1000 dollars, whereof 200 dollar3 is to be for paid present, 400 dollars at 5 months, and the rest at 15 per nionthis, but they agree to make one payment of the whole; I demand when that time must be ? Ans. 8 months.
ре 4. A merchant has due to him a certain sum of money, to be paid one sixth at 2 months, one third at 3 months, ga' and the rest at 6 months ; what is the equated time for the payment of the whole ?
Ans. 41 months. at
of BARTER, IS the exchanging of one commodity for another, and
fro directs merchants and traders how to make the exchange without loss to either party.
Bu Ruhe. Find the value of the commodity whose quantity is given ; then find what quantity of the other at the proposed rate can bulle bought for the same money, and it gives the answer.
1. What quantity of flax at 9 cts. per lb. must be given In barter for 12 lb. of indigo, at 2 dols. 19 cents per lb. ?
12 lb. of indigo at 2 dols. 19 cts, per lb. coines to 26 dols. 28 cts.-therefore, As 9 cts. : 1 lb. : : 20,28 cts. : 292 the answer.
2. How inuch wheat at 1 dol. 25 cts. a bushel, must be given in barter for 50 bushels of rye, at 70 cts. a bustiel ?
Ans, 23 bushels. 3. How much rice at 28s. per cirt. must be bartered for 3 cwt. of raisins, at 5d.
Ans. 5 cæt. 3 qrs. 9:37 11. 4. How much tea at 4s. 9d. per lb. must be given in barter for 78 gallons of brandy, at k2s. 3.4. per gallon ?
Ans. 2011). 13oz. 5. A and B bartered : Ahd 81 cwt. of sugar at 12 cts. per lb. for which 3 gave him 13 cwt. of flour; what was she flour rated ai per lb.
Ans. 5 cts. 6. B delivered 3 hhds. of brandy, at 6s. 8d. per gallon, 80 C, for 126 yds. of cloth, what was the clotlı per yard ?
Ans. 10s, 7. D gives E 250 yards of druggrt, at 30 cts. per yd. sor 319 lbs. of pepper; what does the pepper stand him in
Ans. 23 cts, 51. n. 8. A and B bartered : A had 41 cut. of rice, at 218, per cwt. for which В gave him 201. in money, and the rest in sugar at 8d. per Ib. ; I demand how much sugar B gave A besides the 201. ?
Ans. 6 cut, o
grs. 19,16. 9. Two farmers bartered: A had 120 bushels of wheat at 1} dols. per bushel, for which В gave him 100 bushels of barley, worth 65 cts. per bushel, and the balance in oats at 40 cts. per bushel; what quantity of oats did A receive from B3
Ans. 287} bushels, 10. A hath linen cloth worth 20d. en ell ready money ; but in barter he will have 2s. B liath orcadcloth worth 14s, 6u. per yard ready money, at what price ought B to rate. his broadcloth in barter, so as to be equivalent to A's bartering price?
Ans. 17s. 4d. 37qrs.
per lb. ?
11. A and B barter: A hath 145 gallons of brandy at I dol. 20 cts. per gallon ready money, but in barter die will have 1 dol. 35 cts. per gallon: B has linen at 58 cts, per.yard ready money ; how must B sell his linen per yard in proportion to A's bartering price, and how many yards are equal to A's brandy ?
Ans. Barter price of B's linen is 65 cts. 21m. and he must give A 300 yds. for his brandy.
12. A has 225 yds. of shalloon, at 2s. ready money, per yard, which he barters with B at 2s. 5d. per yard, taking indigo at 12s. 6d. per lb. which is worth but 10s. how much indigo will pay for the shalloon; and who gets the best bargain?
Ans. 43;lb. at barter price will pay for the shalloon, and
£22 10 Value of 43;lb. of indigo, at 10s. per lb. 21 15
B gets the best bargain by £015
3 aga per 1
LOSS AND GAIN, IS a rule by which merchants and traders discover then profit or loss in buying and selling their goods : it also in structs them how to rise or fall in the price of their goods, so as to gain or lose so much per cent. or otherwise.
Questions in this rule are answered by the Rule of Three.
1. Bought a piece of cloth containing 85 yards, for 191 dols. 25 cts. and sold the same at 2 dols. 81 cts. per yard ; what is the profit upon the whole piece?
Ans. $47, 60 cts. 2. Bought 12; cwt. of rice, at 3 dols. 45 cts. a cwt. and sold it again at 4 cts. a pound; what was the whole gain ?
Ans. $12, 87 cts. 5m. 3. Bought 11 cwt. of sugar, at 6 d. per Ib. b it could not sell it again for any more than 21. 16s. per cwt.; did I gain, or lose by my bargain ? Ans. Lost, £2 11s. 41.
4. Bought 44 lb. of tea for 61. 12s. and sold it again for Bl. 10s. 6d. ; what was the profit on each pound?
5. Bought a hhd. of molasses containing 119 gallons, at 52 cents per gallon; paid for carting the same i dollar 25 cents, and by accident 9 gallons leaked out; at what rate must I sell the remainder per gallon, to gain 13 dollars in the whole ?
Ans, 69 cts, 2 m.t
II. To know what is gained or lost per cent. Rule. First see what the gain or loss is hy subtraction; then, As the price it cost : is to the gain or loss : : so is 1001, or $100, to the gain or loss per cent.
EXAMPLES. 1. If I buy Irish linen at 2s. per yard, and sell it again at 2s. 8d. per yard; what do I gain per cent. or in laying out 1001. : As : 2s. 8d, : : 1001. : £:33 Os. 8d. Ans.
2. If I buy broadcloth at 3 dols. 44 cts, per yard, and sell it again at 4 dols. 30 cts. per yard : what do I gain per et. or in laying out 100 dollars?
$ cts. cts.
Ans. 25 per cent.
3. If I buy a cwt. of cotton for 34 dols. 80 cts. and sell it again at 41° cts. per lb. what do I gain or lose, and what
$ cts. 1 cwt. at 41cts. per lb, comes to 46,48
Prime cost 34,86
Gained in the gross, $11,61 As 34,86 ; 11,62 : : 100 : 33. Ans. 33} per cent. 4. Bought sugar at 8:«, per ib, and sold it again at 41. 17s. per cwt. what did I gain per cent. ?
Ars, 25 19s. 571. 5. If I buy 12 huis. of wine for 2041. and sell the same again at 141. 175. 6d. per hhd, do I gain or lose, and what per cent. ?
Ans. I lose 12, per cent, 6. At 1 d. profit in a shilling, how much per cent. ?
Ans. £12 ]Os
per cent. ?