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5. Bought gouds amounting to 615 dols. 75 cents, at 7 months credit; how much ready money must I pay, discount at 41 per cent. per annum?

Ans. $600. 6. What sum of ready money must be received for a bill of 900 dollars, due 73 days hence, discount at 6 per cent. per annum?

Ans. $889, 32 cts. 8 m. Note.- When sundry sums are to be paid at different times, find the Rebate or present worth of each particular payment separately, and when so found, add them into one

sum.

EXAMPLES.

per cent. ?

7. What is the discount of 756l. the one half payable in six months, and the other half in six months after that, at 7

Ans. £37 10s. 2 d. 8. If a legacy is left me of 2000 dollars, of which 500 dols. are payable in 6 months, 800 dols. payable in 1 year, and the rest at the end of 3 years; how much ready money ought I to receive for said legacy, allowing 6 per cent. discount?

Ans. $1833, 37 cts. 4 m.

ANNUITIES.

?

AN Annuity is a sum of money, payable every year, or for a certain number of years, or for ever.

When the debtor keeps the annuity in bis own hands beyond the time of payment, it is said to be in arrears.

The sum of all the annuities for the time they have been foreborne, together with the interest due on each, is called the amount.

If an annuity is bought off, or paid all at once at the beginning of the first year, the price which is paid for it is anlled the present worth.

To find the amount of an annuity at simple interest. RULE.--1. Find the interest of the given annuity for 1 year. 2. And then for 2, 3, &c. years, up to the given time, less 1,

3. Multiply the annuity by the number of years given, and add the product to the whole interest, and the sum will be tho anchini sopgbl.

EXAMPLES.

s.

If an annuity of 701. be forborne 5 years, what will sme due for the principal and interest at the eud of said term, simple interest being computed at 5 per

cent. per annum ?

Yr. .. 1st. Interest of 701. at 5 per cent. for 1-3 10

0 3--10 10

4-14 0 2d. And 5 yrs. annuity, at 701. per yr. is 350 0

Ans. £385 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 wliole term, I demand the sum due at the end of the terni, simple interest being allowed at 6l. per cent. per annum?

Ans. £3301.

To find the present worth of an annuity at simpile

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, tu continue 4 years, at 6 per cent. per annum? 106

377,35849 Pres. worth of let yr. 112

357,14285
: 100 :: 400 :
118

338,98305
322,55064 ==

Bu yii 31 yrs 4th yr.

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124 )

Ans. $1396,06503 $ 1396, 6cts. 5m. 2. How much present money is equivalent to an annuity of 100 dollars, to continue 3 years; rebate being made at per cent. ?

Ans. $268, 37cts. Im. 3. What is 801. yearly rent, to continue 5 years, worth in ready money, at 61.

Ans, £340 15s.to

per cent. ?

EQUATION OF PAYMENTS, IS finding the equated time to pay at once, several debts slue 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 ile several products by the whole debt, and the quotient will be the quated time for the payment of the whole.

EXAMPLES: 1. A owes B 380 dollars, to be paid as follows-viz. 100 lollars in 6 months, 120 dollars in 7 months, and 160 dol Curs in 10 months: What is the equated time for the pay, Fuent of the whole debt?

100 x 6 600
120 X 7 810
160 x 10 1600

330

)3040(8 months. Ans, 2. A m

hant hath owing him 3091. to be paid as fol!ows : 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 Laid 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 liow 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 irgught for the same nxoney, and it gives the answer.

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 Ib. comes to 26 dols. 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 cwt. must be bartered for 31 cwt. of raisius, ut 5d. per lb. ?

Ans. 5 cut. 3 qrs. 9!:276. 4. How much tea at 4s. 9d. per lb. must be given in barter for 78 gallons of brandy, at 12s. 3.d. per gallon?

Ans. 201 lb. 133; oz. 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 ile fiour rated at per lb.

Ans. 5. cts. 6. B delivered 3 hhds. of brandy, at 6s. 8d. per gallon, to C, for 126 yds. of clotli, 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

Ans. 23 cts. 570. 8. A and B bartered : A had 41 cwt. of rice, at 21s. per cwt. for which В gave him 201. in money, and the rest in sugar at 8d. per lb. ; I demand how much sugar B gave A besides the 201. ?

Ans. 6 cwt. O qrs. 1921b. 9. Two farmers bartered: A had 1:20 bushels of wheat nt 1} dols. per bushel, for which В gave himn 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 receive from B?

Ans. 287! bushels. 10. A hath linen cloth worth 200. an ell ready money ; but in barter he will have 23. B bath 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 barJering price ?

Ans. 178. 4d. 3,5grs.

per lb. ?

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 65 cts. 2!m. and he. must give A 300 yds. for his brandy.

12. A has 2:25 yds. of shalloon, at 2s. ready money per yard, which he burters with B at 23. 5d. per yard, taking indigo at 12s. 61. per 1b. 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

21:15

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EXAMPLES.

B gets the best bargain 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 ryle are answered by the Rule of Three.

1. Bought a piece of cloth containing 85 yards, for 191 dols. 25 cts. and sold the same at 2 dols. 81 cts. per yarii ; what is the profit upon the whole piece?

Ans, $47, 60 cts. 2. Bought 12 cwt. of rice, at 3 dolš. 45 cts. a cwt. pel sold it again at 4 cts. a pound; what was the whole gain ?

Ans. $12, 87 ets. 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. Lost, £2, 11s. 4d.

4. Bought 44 lb. of tea for 61. 12s. and sold it again for 81. 10s. 68. ; what was the profit on each pound ?

Ans. 10.11.

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