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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. f. s. 1st. Interest of 701. at 5 per cent. før 1- 10
4-14 0 20. And 5 yrs. annuity, at 7:01. per yr. i3 550
Ans. £585 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 allowed at 6l. per cent. per annuin:
To find the present worth of an annuity at simple interest,
RULE. Find the present worth of each year by itself, discount. ing 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 dots. per annum, to continue 4 years, at 6 per cent. per annum ? 1067
377,35849 Pres. worth of 1st yr. 112
2d yr. 15: 100 :: 400 : 357,14285 338,98305
Sd yr. 124 322,58064
Ans. $1396,06503=81396, 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. $268, 37cts. 1n. 3. What is 801. yearly rent, to continue 5 years, worth in ready money, at 6l. per cent. Ans. £340 15$
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 380 dollars, to be paid as follows-viz. 100 olars in 6 months, 120 dollars in 7 months, and 160 doilars ii 10 months : What is the equated time for the payment of the whole debt.?.
100 X 6 = 600
380 .:'• 130408 months. Ans. 2. A merchant hath owing him sool. 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 timo ? Ans. 6 zonths.
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; 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 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 pro
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. 33 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. 21m. and he must give A 300 yds. for his brandy.
12. A has 225 yds. of shalloon, at 28. ready money, per yard, which he barters with Bat 2s. 5d. per yard, taking indigo at 12s.6d. per Ib. which is worth but 1065. 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 .. 622 10
B gets the best bargain by fQ 15
LOSS AND GAIN, Is a rule by which merehants and traders discover their profit or loss in buying and selling their goods : it also in. structs thein how to rise or fall in the price of their goods, so as to gain or lose so inuch per cent, or otherwise. :) Questions in this rule are answered by the Rule of Three
.: EXAMPLÉS. 1. Bought a piece of cloth containing 85 yards, for 191 dols. 25 cts. and sold the same at 2 dols. 81 ets. per yard; what is the profit upon the whole piece ?
Ans. $47, 60-ts." 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, 87cts. 5m. . 3. Bought 11 cwt. of sugar, at 6 d. per Ib. but could not sell it again for any more than 21. 16s. per cwt. ; did I gain or lose by my bargain ? Ans. Last, £2 11s. 4d..
4. Bought 44 lb. of tea for 6l. 12s. and sold it again for 21. 10s. 6d. ; 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 dollars in the whole ?
his. 69cts. 2m. +
II. To know what is gained or lost per cent.
2. If I buy broadcloth at 3 dols. 44 cts. per yard, and
• Ans. 25 per cent.
S. If 'I buy a cwt. of cotton for 34 dols. 86 ets. and sell It again at 41} cts. per lb. what do I gain or lose, and what per cent. .
$ cts. 1 cwt. at 41 cts. per lb. comes to 46,48
Prime cost 34,86
Gained in the gross, $11,62 As 34,86 : 11,62 : : 100 : 331 Ans. 334 per cent. 4. Bought sugar at 8 d. per Ib. and sold it again at 41. 175. per cwt. what did I gain per cent ?
Ans. £. 25. 195. 5.10. 5. If I buy 12 hhıls, of wine for 2041. and sell the same again at 141. 175. 611. per hhd. do I gain or lose, and what per cent..
Ans. I lose 124 per cent. 6. At 13d. profit in a shilling, how much per cent. ?
Ans. £12 10s.