5. Bought goods amounting to 615 dols. 75 cents, at 7 months credit; how much ready money must I pay, discount at 4 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, 32cts. Sm.

NOTE. When sundry sums are to be paid at differen 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 7561. the one half payable in six months, and the other half in six months after that, at 7 per cent.? Ans. £37 10s. 21d.

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, 37cts. 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 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 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, jess 1.

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

EXAMPLES.

1. If an annuity of 707. 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 eout. per

2d. And 5 yrs. annuity, at 70l. per yr. is

3-10 10

4-14 0

350 0

Ans. £385

2. A house being let upon a lease of 7 years, at 4 dollars per annum, and the rent being in arrear for the whole term, I demand the sum due at the end of the teza, simple interest being allowed at Gl. per cent. per annum ? Ans. £3304.

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

Find the present worth of each year by its If, discounting from the time it falls due, and the sun of all these present worths will be the present worth required

EXAMPLES.

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.

Ans. $1396,06509 $1393, Gets 5mm.

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. 3. What is 801. yearly rent, to continue 5 years, worth in ready money, at 61, per cent. ? Ans. £340 15s. +

M*

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 dol lars in 10 months: What is the equated time for the pay ment of the whole debt ?

2. A merchant hath owing him 300l. to be paid as fol lows: 50l. at 2 months, 1007. 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 pay ment of the whole? Ans. 4 months

BARTER,

Is the exchanging of one commodity for another, and die

rects merchants and traders how to make the exchange without loss to either party.

?

RULE.

Find the value of the commodity whose quantity is giv

then find what quantity of the other at the pro

posed 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 12 lb. of indigo, at 2 dols. 19 cts. per lb. ? 12 lb. of indigo at 2 dols. 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 3 cwt. of raisins, at 5d. per lb. ?

336

Ans. 5cwt 3qrs. 911lb. 4. How much tea at 4s. 9d. per lb. must be given in barter for 78 gallons of brandy, at 12s. 34d per gallon? Ans. 2016. 13340%.

5. A and B bartered: A had 84 cwt. of sugar at 12 cts. per lb. for which B gave him 18 cwt. of flour; what was the flour rated at per lb. ? Ans. 51cts.

6. B delivered 3 hhds. of brandy, at 6s. 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 30 cts. per yd for 319 lbs. of pepper; what does the pepper stand him in per lb. Ans. 23cts. 5m. 8. A and B bartered: A had 41 cwt. of rice, at 21s. per cwt. for which B gave him 201. in money, and the rest in sugar at 8d. I demand how much sugar B lb. per ; gave A besides the 201. ? Ans. 6cwt. Ogrs. 191lb. 9. Two farmers bartered: A had 120 bushels of wheat at 11 dols. per bushel, for which B gave him 100 bushels of barley, worth 65 cts. per bushel, and the balance in oats at 40 cis. per bushel; what quantity of oats did A receive from B? Ans. 287 bushels.

10. A hath linen cloth worth 20d. an el ready money; but in barter he will have 2s. 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. 178. 4d. 3,3qrs.

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 65cts. 24m. 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 2s. 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. 431b. at barter price will pay for the shalloon, and B has the advantage in barter

Value of A's cloth at cash price, is

Value of 431lb. of indigo, at 10s. per lb.

£22

10 21 15

B. gets the best bargair. 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 rule are answered by the Rule of Three.

EXAMPLES.

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 121 cwt. of rice, at 3 dols. 45 cts. a.cwt. and sold it again at 4 ets. a pound; what was the whole gain? Ans. $12, 87cts. 5m. 3. Bought 11 cwt. of sugar, at 6d. per lb. but could not sell it again for any more than 27. 16s. per cwt. ; did I gain or lose by my bargain? Ans. Lost, £2 11s. 4d. 4. Bought 44 lb. of tea for 67. 12s. and sold it again for 87 10s. 6d. ; what was the profit on each pound?

Ans. 101d