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EXAMPLES. If an annuity of 701. be forbore 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 innum ?
Yr. £. S. Ist. Interest of 701. at 5 per cent. for 1- 3 10
2- 7 0 3-10 10
1-14 0 20. And 5 yrs. annuity, at 701. jei yr. is 3500
• Ans. £335 0 2. A house being let upon a lease of 7 year3, 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 61. per cent. per annum
To find the present worth of un annuity at simple
interest. Rule. Find the present worth of each yeur by itself, discounting from the time it falls due, and the sun of all these present worths will be the present worth required.
EXAMPLES 1. What is the present worth of 400 dols. per annum, to continue 4 years, at 6 per cent. per annum? 1067
377,35849 = Pres. worth of 1st yr. 357,14285 =
2d yr. 118
3d yr. 124) . : 322,58064 =
4th yr. Ans. $1396,0650,3 = $13!1i, Octs. 5m. 2. How niuch present money i; equivalent to an annuity of 100 dollars, to continue 3 years; rebate being made at 0 per cent. ?
Ins. $268, 37 cts. 3. What is 801. yearly rent, to continue 5 years, worht in ready m mney, ε.t 6l. per cent. Ans. £340, 5s 4d.
EQUATION OF PAYMENTS,
IS finding the equated time to pay at once, several debts Que at different periods of time, so that no loss shall be! sustained by either party.
Rule.-Multiply cach payment by its time, and divide the suni if: the several products by the whole debt, and the quotient will be the equated time for the payment of the whole.
EXAMPLES. 1. A owes B 380 dollars, to be paid as follows-viz. 1001 dollars in 6 months, 120 dollars in 7 months, and 160 dol. Jars in 10 niontlis: What is the equated time for the pay. ment of the whole debt ?
100 X 6 = 600
3040(8 months. ns. t. %. A merchant bath owing him 3001. to be paid as fól lows: 501. at 2 months, 1001. at 5 months, and the rest. č.p. 8 months; and it is agreed to make one p:iyment of the whole: I demand the equated time? Ans. 6 months.
3. F owes H 1000 dollars, whereot 200 dollars is to her paid present, 400 dollars at 5 months, and the rest at 1.34 nionths, but they agree to make one payment of the whole; I demand when that time must be ? Ans. 8 months, :
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, and the rest at 6 months; what is the equated time for the payment of the whole ?
Ans. 4 months. 3}}
BARTER, IS the exchanging of one commodity for another, and" directs merchants and traders how to make the exchange without loss to either party.
otto Rule. Find the value of the commodity whose quantity is given then find what quantity of the other at the proposed rate can bo". bought for the same money, and it gives the answor.
EXAMPLES. 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 Ib. ?
12 lb. of indigo at 2 dols. 19 cts. per lb. comes to 26 dols. 28 cts. therefore, As 9 cts. : 1 lb. : : 20,28 cts. : 292 the answer.
2.2. How much wheat at I dol. 25 cts. a bushel, must be given in barter for 50 bushels of rye, at 70 cts. a bushel ?
Ans. 23 bushels. 3. How much rice at 28s. per cwt. must be bartered for 3. cwt. of raisins, at 5d. per Ib. ?
Ans, 5 cwt, 3 grs. 9.!!? lb. 4. How much tea at 4s. Id. per lb. must be given in barter for 78 gallons of brandy, at 12s. 3 d. per gallon ?
Ans. 201 lb. 131 oz. 5. A and B bartered: A Jond 81 cwt. of sugar at 12 cts. per lb. for which 3 gave him 13 cwt. of flour; what was he flour rated a. per lb.
Ans. 5 cts. 6. B delivered 3 bhds. of brandy, at 6s. 8d. per gallon, 1. C, for 126 yds. of clothi, what was the cloth per yard ?
Ans. 10s. 7. D gives E 250 yards of drugget, at 30 cts. per yd. jor 319 Jbs. of pepper; what does the pepper stand hin in per lb. ?
Ans: 23 cts. 51.m. 8. A and B bartered : A bad 41 cwt. of ricc, at 21s. 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 cwt. 0 grs. 19 lb.
9. Two farmers bartered: A had 120 bushels of wheilt ut 1} dols. per bushel, for which В gave him 100 buslicls 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 B?
Ans. 2871 bushels. 10. A hath linen cloth worth 20d. en ell ready money ; but in barter he will have 2s. B hath broadcloth 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 hartering price?
Ans. 17s. 411. 34 qrs.
11. Å and B burter: I hath 1.45 yillons of brands :). I dol. 20 cts. per gallon ready money, but in barter le will have 1 dol. 35 cts. per gallon: Blas linen at 58 cts, per yard ready money ; how must B sell his linen pe: 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 6.5 cts. 297. 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 Rs. 5d. per yard, taking indigo at 12s. 60. 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 B has the advantage in barter. Value of A's cloth, at cash price, is
£22 10 Value of 43;lb. of indigo, at 10s. per lb. 21
B gets the best bargain by
LOSS AND GAIN, IS a rule by which merchants and traders discover their 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 Threc.
EXAMPLES. 1. Bought a piece of cloth containing 85 yards, for 191 dols. 25 cts. and sold the same at 2 cols. 81 cts. per yard ; what is the profit upon the whole piece?
Ans. $.17, 60 ct.. 2. Bought 12 cwt. of rice, at 3 dols. 45 cts. a cwt anda sold it again at 4 cts. a pound; what was the whole gain 1
Ans. $12, 87 cts. 5m. 3. Bought Il cwt. of sugar, at (dl. per 1b, bit could nol. soil it again for any more than 21. 16s. per cwt.; did I gam or lose by my bargain ? Ans. Lost, £2 lls. 4il.
4. Bought 44 lb. of tea for 61. 12s. am sold it again for 21. 10s. 61. ; what was 1!ie profit on each pounded?
..). Bougit a bhd. of molasses containing 119 gallons, af 52 cents per gallon; paid for carting the same 1 dollar 25 cents, and by accident 9 gallous leaked out ; at what táte must I sell the remainder per gallon, to gain 13 dollars in the whole?
Ans. 69 cts. 2 m. +
II. To know what is gained or lost per cent. Rule. First see what the gain or loss is by 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. &d. : : 1001. : £33 6s. 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 ct. vi in laying out 100 dollars? ibi
Ans. 25 per cent.
3. If I buy a cwt. of cotton for 34 dcls. 86 cts. and sell it again at 41; cis. per lb. what do I gain or lose, and what per cent. ?
$* cts. . ** 1 cwt. at 411 cts. per Ib. comes to 46,48
Prime cost 34,86 .
Gained in the gross, $11,61 As 34,86 : 11,62 : : 100 : 331 Ans. 33į per cent. 4. Bought sugar at 8 d. per lb, and sold it again at 41. 178. per cwt. wliat did I gain per cent. ?
Ans. £25 19s. 5 d. 5. If I buy 12 blads, of wine for 2041. and sell the same again at 141. 17s. 6d. per hlıd. do I gain or lose, and what per cent. ?
Ans. I lose 121 per cent. 6. At lfd. profit in a shilling, how much per cent. ?
Ans. £12 10s.