EXIPLES. 1. If an annuity of 701. be forborne 5 years, what will be due for the principal and interest at thg end of said term, sirople interest being computed at 5 per cent. per annum ? Ir. , £. s. ist. Interest of 701. at 5.,por cent. for 1-3 10 3-10 10 414 0 21. An 5 yrs. annuity, at 70l. per yr. is $50 0 Ins. £585 1 2. A house being let upon a lease of 7 years, at 400 dollars per annum, and the rent ling in arrear for the whole term, I demand the sum due at the cnd of the term, simple interest being allowed at 6l. per cent. per annuin ? Ans. $5304. 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 suin of all these present worths will be the present worth required, EXAMPLES. 1. iVhat 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 112 : 100 :: 400 : 357,14285 118 338,98305 124 S29,58064 2d yr. 4th yr. 3rs. S1396,06503=S1596, Octs. Jh. 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, 37cts. 1m. 8. What is 80l. yearly rent, to continue 5 years, worthi di ready money, at 6l. per cent. Ans. f,S40 155. -47 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 sustained by either party. RULE. Multiply each payment by its time, and divide the sum of 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 580 dollars, to be paid as follows-viz. 100 dallars in 6 months, 120 dollars in 7 months, and 160 dollars in 10 months : What is the equated time for the payment of the whole debt? 100 X 6 600 120 x 840 160 X 10 s 1600 S80 3040(8 months. Ans. . A merchant hath owing him 500l. to be paid as fol. iows: 501. at 2 months, 1001. at 5 months, and the rest at 8 months; and it is agreed to make one payment of the whole ; I demand the equated time? Ans. 6 months. 3. F owes II 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5 months, and the rest at 15 inonths, 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. BARTER, Is the exchanging of one commodity for another, and directs merchants and traders low to make the exchange without loss to either party. RULE. Eind the value of the commodity whose quantity is giren; then find what quantity of the other at the pro nosedl rate can be bought for the same money, and it gives the answer. EXAMPLES. 1. What quantity of flax at 9 cts. per lb. must be given in barter for 12lb. of indigo, at 2 dols. 19 cts. per lb. ? 121b. of indigo at 2 dols. 19 cts. per lb. comes to 26 dols. 28 cts.-therefore, As 9 cts. i llb. : : 26,28 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 bushel ? Ans. 28 busheis. 3. How much rice at 28s. per cut. must be bartered for Sicwt. of raisins, at 5d. per lb. ? Ans. 5cut. 3qrs. 94}zló. 4. How much tea at 45. 9d. per lb. must be given in barter for 78 gallons of brandy, at 125. 31d. per gallon ? Ans. 2011b. 1537oz. 5. A and B bartered : A had 8!cwt. of sugar at 12 cts per lb. for which В gave him 18cwt. of flour; what was the flour rated at per Airs. 5jcts. 6. B delivered S hhds. of brandy, at Os. Sd. per gallon, to C, for 126 yds. of clothi, what was the cloth per yard 7. D gives E 250 yards of druget, at so cts. For yd. for 31916. of pepper; what does the pepper star hin in fer lb. i s. 236. 7. 8. A and B barterni: si ha dicwi, oi ricen se per cwt. for which В gave lion 20%. in nudi rest in sugar, at 8d. per ib. ; i demand how to B gave A besides the 201. Ans. Gout. Ogr. 9:19. 9. Two farmers bartered: A had 120 basliels of wheat at 11 dols. per bushel, for which В gave him 100 buste. of barley, worth 65 cts. per bushel, and the balance in cais at 40 cts. per buslici; what quantity of oats did A receives from B? Ans. 287 } bushev 10. A hath linen cloth worth 20d. an ell ready money: but in barter he will have 2s, B hath broadcloth worth 145. 6d. per yari ready money, at what price ought B to rata luis broadcloth in barter, so as to be equivalent to A's bertering price? Ins. 173. 64. Sears. A and B barter: A nath 145 gallons of brandy at A. 20 cts. per gallon ready money, but in barter he ill 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 25. ready money; per yard, which he barters with B at 2s. 511. per yar), talis 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 B has the advantage in barter. Value of A's cloth at cash price, is 1.5 B gets the best bargain by 10 15 EXAMPLES. 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, 80 as to gain or lose so much per cent. or otherwise. Questions in this nile are answered by the Rule of Throt. 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 12 cwt. of rice, at 3 dols. 45 cts. a cut. and sold it again at 4 cts. a pound; what was the whole Ans. $12, 87 cts. 5m 3. Bought 11 cwt. of sugar, at God. per Ib. but could not sell it again for any more than 2. 16s. per cwt.; sljel 1 gain or lose by my bargain ? Ans. Lost, .2 11s. 4d. 4. Bought 44 lb. of tea for 6l. 125. and soll it again for 81. 10s. 611.; wliat was thc profit on each pound ? Ans. 104. gain 5. Bought a hhd. of molasses containing 119 gallons, et 52 cts. per gallon; paid for carting the same i dollar 25 cents, and by accident 9 gallons leaked out; at what Fate must I sell the remainder per gallon, to gain 13 dol lars in the whole ? Ans. 69cts. 2m.-t 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 23. 8d. per yard; what do I gain per cent. or in laying out 1001. : Ås : 2s. 8d. : : 100l. : £35 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 ? S cts. $ cts. cts. S As 3, 44 : 86 : : 100, : 2014 Ans. 25 per cent. Gained per yd. 86 3. If I buy a cwt. of cotton for 34 dols. 86 cts. and sell it again at 413 cts. per Ib. what do I gain or losc, and what Sots. 1cwt. at 41 cts. per Ib. comes to 46,48 Prime cost 34,86 3, 44 per cent. . Gained in the gross, $11,62 As 54,86 : 11,62 : : 100 : 33} Ans. 33} per cent. 4. Bought sugar at 81d. por ib. and sold it again at 41. 178. per cwt. what did I gain per cent. ? Fins. £25 19s. 53d. 5. If I buy 12 hhds, of wine for 204l. and sell the same again at 141. 17s. 6d. per hhd. do I gain or lose, and what Ans. I lose 12 per cent. 6. At 13d. profit in a shilling, how much per cent. ? Ans. £12 10s. per cent. P. |