EXAMPLES. Yr. £. s. 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 } 1st. Interest of 70l. at 5 per cent. for 1- 3 10 2- 7 0 3-10 10 414 0 2d. And 5 yrs. annuity, at-701. per yr. is 350 0 Ans. $385 0 400€ 2. A house being let upon a lease of 7 years, at cephors 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 allowed at 6l. per cent. per annum ? Ans. £3304. Tn 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 sum 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 ? 106 377,35849 Pres. worth of Ist yr. 112 357,14285 : 100.. 400: 118 338,98305 124 322,58064 = 2d yr 3d yr. 4th yr. Ans. $1396,06503=$1396, 6cts. 5m. 2. How much prosent money is equivalent to an annuity of 100 dollars, to continue 3 years ; rebate being made at 6 per cent; ? Ans. $268, 37cts im. 3. Wliat is sol. yearly rent, to continue 5 years, worth in ready money, at 61. per cent. ? Ans. 840 153,-* EQUATION OF PAYMENTS, Is finding the cquated time to pay at once, several debie due at different periods of time, so that no loss shall be sus tained by either party. RULE. Multiply each payment by its time, and dinge Sie sum of the several products by the whole debt. *d toe quotient will be the equated time to the paymeki of tae whole. EXAMPLES. 1. A ores B 380 dollars, to be paid as follows-viz. 100 dollars in 6 months, 120 dollars in 7 months, and 160 dollars in 10 months : What is the equated time for the pay dient of the whole debt ? 100 X 6 600 7 840 whole ; 380 )3040(8 months. Ans. 2. A merchant hath owing him 3001. to be paid as fol lows : 501. at 2 months, 1001. at 5 months, and the rest at 8 months; and it is agreed to make one payment of the I demand the equated time ? ins. 6 months. 3. Y owes H 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5 months, and the rest at 15 months, b'n 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 th.. 3 months, and the rest at 6 months ; what is the equated time for the pay. ment of the whole ? Ans. 4 months RARTER, Is the exchanging of one commodity for another, and di fects merchants and traders hno to make the exchange with out loss to either party RULE. Find the valun of the commodity whuge quantity is given wa; Nano find what quantity of the other at the pro posed rate can be bought for the same money, and it girca the answer. EXAMPLES. 1. What quantity of flax at 9 cts. per lb. must be giya en in barter for 12 lb. of indigo, at 2 dois. 19 cts. per lb. ? 12 lb. of indigo at 2 dols. 19 cts. per lb. comes to 20 dob. 28 cts.--therefore, As 9 cts. : 1 lb. : : 26,28 cts. : 292 the answer. 2. How much wheat at 1 dol: 25 cts. a bushel, must be given in barter for 50 bushels of rye, at 70 cts. a bushel ? Ans. 28 bushels. 3. How much rice at 28s. per cvt. must be bartered for Scwt. of raisins, at 5d. per Ib. ? Ans. 5cwt 3qrs. 937 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. 2011b. 1337oz. 5. A and B bartered : A had 81 cwt. of sugar at 12 cts. per lb. for which В gave him 18 cwt. of flour ; what was the flour rated at per lb. ? Ans. 5 ct. 6. B delivered 3 hhds. of brandy, at 6s. 8d. per gallon, to C, for 126 yds. of cloth, what was the cloth per yard ? Ans. 10s. 7. D gives E 250 yards of drugget, at 30 cts. per yd. for 319 lbs. of pepper; what does the pepper stand him in perlb. Ans. 23cts. 51, n. 8. A and B bartered : A had 41 cyt. of rice, at 2s. per cwt. for which В gave him 201. in money, rest in sugar at 8d. per lb. ; i demand how much sugar B gave A besides the 201. ? Ans. Ocut. Oqrs. 1916. 9. Two farmers bartered : A had 120 busliels 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 re. ceive from B ? Ans. 287 bushels. 10. A hath linen cloth worth 20d an ell ready money ; but in barter he will have 23. B hath broadcloth worth 14s. 6d. per yard ready money, at what price o'ght B to rate his broadcloth in Irarter, so as to be equivadent to A's bartering paca? Ars. I78, Ad vigre, and 11. A and B barter : A hath 145 gallons of brandy at 1 dol. 20 cts. per gallon ready money, but in barter he 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 65cts. 2 m. 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. 431/b. 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 15 B. gets the kest bargair. by £0 15 LOSS AND GAIN, IS a rule by which merchants and traders discover their profit or loss in buying and selling their goods : it also instructs 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. EXAMPLES. 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, 60cts. 2. Bought 121 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, 87cte. 5m. 3. Bought 11 cit. of sugar, at f£d. per lb. but could not sell it again for any more than 21. 10s. per cwt. ; did I gain or lose by my bargain ? Ans. Lost, £2 11s. 4d. 4. Bought 44 ib. of tea for 61. 12s. and sold it again for 8l. 10s. 6d. ; what was the profit on each pound ? Ans. 1014 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 dol lars in the whole ? Ans. 69cts. 20. 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. gr $100, to the gain or loss per cent. EXAMPLES. . 3, 44 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 : 28. 8d. : : 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 cent. or in laying out 100 dollars ? $ cts. Sold for, 4, 30 $ cta. cts. Cost As 3, 44 : 86 : 100 : 25 Ans. 25 per cent. Gained per yd. 86 3. If I buy a cwt. of cotton for 34 duls. 86cts. and sell it again at 414 cts. per lb. what do I gain or lose, and what $ cts. 1 cwt. at 41 os. per lb. comes to 46,48 Prime cost 34,86 Gained in the gross, $11,62 As 34,86 : 11,62 : ; 100 : 33} Ans. 33} per cent. 4. Bought sugar at 8 d. per lb. and sold it again at 4h 17's. s. per cwt. what did I gain per cent. ? Ans. £25 195. 59 d. 5. If I buy 12 hhds of wine for 2041. and sell the same again at 141. 17s. Od. A hhd do I gain or lose, and wtrat per cent. ? Ans. I lose 12.per cent. 6. Atl;d. profit in i shilling, how much per cent. ? Ans, £ 12 10 per cent. ? |