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 75 days hence, discount at 6 per eent. per annum? Ans. $889, 32cts. 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 750l. the one half payable in six months, and the other half in six months after that, at 7 per cent.? Ans. £37 10s. 24d.

8. If a legacy is left me of 2000 dollars, of which 500 dols. are payable in 6 months, 800 dois. 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, 7cts. 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.

5. 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 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 ?

1st. Interest of 70l. at 5 per cent. for

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

Yr. £. s.

1-3 10 2- 7. 0 3-10 10 4-14

0

350 0

Ans. £385 0

. 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, simpe interest being allowed at 61. per cent. per annum? Ars. $3304.

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.

Ans. $1396,06503=$1396, 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. 1m. 3. What is 801. yearly rent, to continue 5 years, worth m ready money, at 6. per cent. Ans. £340 15s

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

7 =

840

160 x 10 = 1600

380

)5040(8 months. Ins.

2. A merchant hath owing him 300l. to be paid as follows: 50l. at 2 months, 100l. 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. Fowes II 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

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. ? 19 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. bushel?

Ans. 28 bushels.

3. How much rice at 28s. per cwt. must be bartered for 3 cwt. of raisins, at 5d.

per lb.?

in

Ans. 5cwt. 3qrs. 9112lb. 4. How much tea at 4s. 9d. per lb. must be given barter for 78 gallons of brandy, at 12s. 34d. per gallon? Ans. 201lb. 13270z.

5. A and B bartered: A had & 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. 53cts.

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 519 lbs. of pepper; what does the pepper stand him per lb. ? Ans. 23cts. 5m.

in

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. per lb. ; I demand how much sugar B gave A besides the 201.? Ans. 6cut. Oqrs. 19 lb.

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 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 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. 17s. 4d. Syrs.

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

ins. 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 23. 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. 43lb. 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 43 lb. of indigo, at 10s. per lb.

£22 10

21 15

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 rule are answered by the Rule of Threo

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 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 P Ans. $12, 87cts. 5m. 3. Bought 11 cwt. of sugar, at 64d. per lb. 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 6l. 12s. and sold it again for V. 10s. 6d.; what was the profit on each pound? Ans. 10 d.