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EXAMPLES 1. It 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. 6. s. 1st. Interest of 701. at 5 per cent. for 1-3 10
27 0 3-10 10
4-14 0 2d. And 5 yrs. annuity, at 70l. per yr. is 350 0
Ans. £385 0 L. A house being let upon a lease of 7 years, at 400 dollars per annum, and the rent being in arrear for the who.e term, I demand the sum due at the end of the term, simple interest being allowed at 6l. 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 sum 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 =
2d yr. : 100 :: 400 : 118 338,98305
sd yr. 124
Ans. $1396,06503=$1996, 6cts. 5m. 2. How much present money is equivalent to an an nuity of 100 dollars, to continue 3 years ; rebate being made at 6 per cent. ?
Ans. $268, 37 cts. Im. 3. What is 801. yearly rent, to continue 5 years, worth m ready money, at 6. per cent. Ans. £340 158 +
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.
1. A owes 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 payment of the whole debt ?
100 X 6 = 600
)3040(8 months. Ans, 2. A merchant hath owing him 3001. to be paid as follows : 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 H 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5 months, and the rest at 15 months, but they agree to make one payment of the whole;
. 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 how to make the exchange without loss to either party.
RULE. Find the value of the commodity whose quantity is given; then find what quantity of the other at the proposed rate can be 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 cts. per Ib. ?
12 lb. of indigo at 2 dols. 19 cts. per lb. comes to 26 dols. 28 cts.--therefore, As 9 cts. : i 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 288. per cwt. must be bartered for 33 cwt. of raisins, at 5d. per
Ans. 5cwt. Sgrs. 94131h. 4. How much tea at 4s. 9d. per lb. must be given in barter for 78 gallons of brandy, at 12s. 3d. per gallon ?
Ans. 2011b. 133702. 5. A and B bartered : A had & cwt. of sugar at 12 cts. per lb. for which В gave him 18 cwt. of flour ; what was the flour rated at
Ans. vlcts. B delivered 3 hhds. of brandy, at 68. 84. per gallon, to C, for 126 yds. of clothi, what was the cloth per yard ?
Ans. ios. 7. D gives E 250 yards of drugget, at 50 cts. per yd. for 319 lbs. of pepper ;' what does the pepper stand iiim in per Ib. ?
Ans. 23cts. 5jom. 8. A and B bartered : A had 41 cwt. of rice, at 21s, per cwt. for which В gave himn 201. in money, and the rest in sugar at 8d. per
I demand how much sugar B gave A besides the 201. ?
Ans. 6cwt. Oqrs. 19 alb. 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 cats at 40 cts. per bushel ; what quantity of oats did A receive from B. ?
Ans. 287} bushels. 10. A hath linen cloth worth 20d. an ell ready money, but in harter he will have as. B hath broadcloth worth 14s. 6d. 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. 4.1. .
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. der yard ready money; how must B sell his linen per yard in proportion to Å's bartering price; and how many yards are equal to A's brandy ?
Ans. Barter price of B's linen is 65cts. 23m. 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 28. 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. 433lb. at barter price will pay for the -shalloon, and B has the advantage in barter.
Value of 'A's cloth at cash price, is
21. 15 B gets the best bargain by £015
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
1. Bought a piece of cloth containing 85 yards, for 19 Mols. 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 cwt. and sold it again at 4 cts. a pound; what was the whole gain?
Ans. $12, 87cts. 5m. 3. Bought 11 cwt. of sugar, at 6 d. per lb. but could not sell it again for any more than 21. 165. per cwt.; did I gain or lose by my bargain ? Ans. Lost, £2 11s. 4d.
4. Bought 44 lb. of tea for 6l. 12s. and sold it again for kl. 10s. 60.; what was the profit on each pound ?
5. Bought a hhd. of molasses containing 119 gallons, at 52 cts. 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. 2m.
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 100l. or 8100, to the gain or loss per cent.
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 6s. 8d. Ans.
2. If I buy broadcloth at 3 duls. 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 ?
8. cts. cts. 8 S
As 3, 44 : 86 : : 100 : 25
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 414 cts. per lb. what do I gain or lose, and what per cent. ?
$ cts. 1 cwt. at 414 cts. per lb. coines 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 8fd. per lb. and sold it again at 41, 17s. per cut. what did I gain per cent. ?
Ans. £,25 19s. 5fd. 5. If I buy 12 hhıls. of wine for 2011. and sell the same again at 141. 173. 6d. per hhd. do 1 gain or lose, and what per cent. ?
Ans. I lose 12, per cent. 6. At 14d. profit in a shilling, how much per cent. ?
Ans. £12 !