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

Ans. 8600. 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. 8889, Sects. 8m. 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.

7. What is the discount of 7507. the one half payable in six months, and the other half in six months after that, at 7 per cent. ?

Ans. £37 10s. 23d. 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. 4m.

ANNUITIES. An Annuity is a sum of money, payable every year, or for a certain number of years, or forever.

When the debtor keeps the annuity in his 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 forborne, 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 called 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 svill be the amount sought.

EXAMPLES.

1, If an annuity of 701. be forborne 5 years, what will be due for the principal and interest at the end of said lerm, simp'e interest being computed at 5 per cent. per amimni

1. • S. 1st. isierest of 701. ai 5 per cent. for 13 10

20 Sm1() 10

-14 0 Pu. And 5 yrs. annuity, at 701. per yr. is 550 0

Ans. £385 0 .. A house being let upon a lease of 7 years, at 400 Jol ars per annum, and the rent being in arrear for the whole teim, I demand the süni due at the end of the term, sune interest being allowed at bil. per cent. per annuin?

dis. $3304.

To find the present worth of an annuity at simple interest.

RlIE. Find the present worth of each year by itself, discount ing from the time it falls dre, atil the sum of all these present worths will be the present worth required.

EXAMPLFS.

1. What is the present worth of 400 dols. per annum, to continue 4 ycars, at 6 per cent. per annum: 1069

37:135849 = 'Pres. worth of 1st yr 112

35.,14:283 = : 100 :: 400 : 118 358,98505 =

5c! sr. 124

322,38064

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4th yr.

Ans. S1596.0650391396, Octs. 5m. ... How mucli present movies is equivalent to an an nuity of 100 doiliers, to continue 3 years; rebate bring maile at 6 per cerit. i

Ans. $268, 57043. Im. 3. What is 80l. yearly rent, tu coritinue 3 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.

EXAMPLES.

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
120 X

840
160 x 10 = 1600

7

380

) S040(8 months. uns. 2. A merchant hath owing him 300l. 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; 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 preposed rate can be bought for the same money, and it gives the answer.

EXAMFLES.

1. What quantity of flax at 9 cts. per lb. must be given in barter for 12 Ib. of indigo, at 2 dols. 19 cts. per lb. ?

12 lb. of indigo at 2 dois. 19 cts, per lb. 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 S} cwt. of raisins, at 5d. per lb. ?

Ans. 5cwt. Sqrs. 9443lh. 4. How much tea at 4s. 9d. per lb. must be given in barter for 78 gallons of brandy, at 12s. 31d. per gallon ?

Ans. 2011b. 13 Loz. 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 per lb. ?

Ans. 5}cts. 6. B delivered 3 hhds. of brandy, at 69. 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 50 cts. per yd. for 319 lbs. of pepper; what does the pepper

stand nim in per

Ans. 23cts. 5 bin. 3. A and B bartered: A had 41 cwt. of rice, at 21.s. per

cwt. for which В gave him 201. in money, and the rest in sugar at 8d. per

I demand how much sugar B gave A besides the 201. ? Ans. 6cwt. Ogrs. 1931b.

9. Two farmers bartered : A had 120 bushels of wheat, at 11 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 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?

Axs. 175. 4d. 310478.

Ib. ?

Ib. ;

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. 55 Cis. per gallon: B has linen at 58 cts. der yard ready money; how must B sell his linen per yard in priportion to A's bartering price, and how many yards are equal to A's brandy?

Aris. Barter price of B's linen is €5cts. 23m. and he must give A 500 yds. for his brandy.

12. A has 225 yds. of shalloon, at 2s. ready money, per yard, which he barters with B at 23. 5d. per yard, taking imigo at 12s. 6d. per lb). which is worth but los. how much indigo will pay for the shalloon; and who gets the best bargain

Ans. 434_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 622 10 Value of 43;lb. of indigo, at 10s. per lb. 21 15

B gets the best bargain by 10 15

EXAMPLE.S.

LOSS AND GAIN, Is a rule by which merchants and traders discover their profit or loss in buying and selling their goods : it also ille structs them how to rise ur tall in the price of their gorais 50 as lu gain or lose so much per cent. or otherwise Questions in this rule are answered by the Rule of Three 5:17://

1. Bought a piece of cloth containing 35 yards, for 191 dels 23 cts. and sold ine same at 2 cols. 81 cts. per yard; what is the profit upon the whole paece:

otro. , 60:ës. 2. Bought 125 cut. of rice, at 3 cols 45 cts, a cute and sold it again at 4 cts. a pound; what was the whole

. ?ns. $12. Wirts. im. S. Benght 11 cwt. of sugar, at figoli pes llo. :11t couil not seil ir ayniu fior any more t’an 21:n p"; . illu 1

gain or in-p by mylargu! 3us. Loiste lis tib.

4. Burghie tilsinfirä fue Cl. s. aint suint it 36. lus. vd.: what was the porudio us each jound :

gain :

again for

Hus 101.

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