$200.00

Philadelphia, 8th mo. 3d, 1844. Sixty days from date, I promise to pay Pliny E. Chase, or order, two hundred dollars, for value received.

$144.00

WILLIAM JACOBSON.

Baltimore, Aug. 1, 1844.

Ninety days from date, I promise to pay Pliny E. Chase, or order, one hundred and forty-four dollars, for value reGEORGE M. WATSON.

ceived.

$75.75

New York, Sept. 5, 1844.

Six months from date, I promise to pay Pliny E. Chase, or order, seventy-five dollars and seventy-five cents, for value received. MARCUS GRAHAM.

7. What is the bank discount on a note of $1270 for 30 days? 60 days? 120 days?

8. What is the difference between the equitable and the bank discount on $2000 for 1 year?

9. How much do I gain by purchasing molasses for $1600 cash, and selling it immediately for $2000, payable in 9 months, the People's Bank discounting the note at 7 per cent.?

10. Sold George Manning & Brothers, 61cwt. of sugar, at 51⁄2cts. a pound; 81 barrels of flour, at $4.621⁄2 per barrel; 3.679cwt. of coffee, at 8cts. a pound; 2cwt. 1qr. 17lb. of rice, at $3.50 per cwt.; 13 boxes sperm candles, each containing 324lb., at 293cts. per lb.; and 19lb. 11oz. chocolate, at 183cts. a pound. How much was received on their note for the amount, at 90 days, discounted at the National Bank ?

11. Sold Clark & Atkins, 3cwt. 1qr. 17lb. of sugar, at $5.00 per cwt.; 3913lb. Young Hyson tea, at 871cts. a pound; 250lb. Imperial tea, at 637cts. a pound; 78gal. 3qt. of molasses, at 311cts. a gallon; and 1273lb. cheese, at 83cts. a pound, receiving their note at 120 days for the amount. What is the value of the note, discounting at 7 per cent.?

12. What is the value of a note at 60 days, for the following amounts? 163ğyd. of silk, at 871⁄2cts. a yard,

4911yd. India muslins, at 621cts. a yard; 3633yd. Alpacca, at 933cts. a yard; 224yd. merino, at 50cts. a yard; and 251 gyd. printed lawn, at 371⁄2cts. a yard.

13. What is the value of a note at 30 days, for $24491. 75, discounting at 5 per cent.?

14. What is the value of a note at 60 days, for $1874.50, discounting at 4 per cent.?

15. What is the value of a note at 90 days, for $4959. 375, discounting at 47 per cent.?

16. What is the value of for $7638, discounting at 51

of of a note at 120 days, per cent.?

17. What is the value of of of a note at 30 days, for $10000, discounting at 71 per cent.?

18. What is the value of of .97 of 8 of a note at 4 months, for £2610 7s. 6d., discounting at 5 per cent.?

19. A merchant has five notes at 60 days, of equal value, amounting in the whole to £197631. What is the worth of .85 of one of them, in pounds, shillings and pence, discounting at 41 per cent.?

20. What is the value of a note at 6 months, for $1175. 875, discounting at 83 per cent.?

CHAPTER X.

EQUATION OF PAYMENTS AND AVERAGE.

When several debts are due at different times, it is often desirable to find some time at which they may all be paid, without loss to either the debtor or the creditor. This time is called the AVERAGE, or EQUATED TIME, and the process by which it is found is the EQUATION OF PAY

MENTS.

EXAMPLE FOR THE BOARD.

A merchant owes $4.00, payable in 3 months; $6.00 payable in 6 months, and $2.00 payable in a year. At what time may he pay the whole, so that neither party shall lose any in

terest?

1

He may keep $12.00, as long as $1.00. Therefore, dividing 72mo. by 12, we obtain 6mo. for the equated time.

RULE.

Multiply each debt by the time in which it is payable, add all the products, and divide their sum by the sum of the debts.

This rule, which is universally adopted, is founded on the supposition that the interest of the money, which is not paid until after it is due, is equal to the discount of that which is paid before it is due. This is not strictly correct, but the difference is so trifling, that it does not materially affect the ordinary transactions of business.

1. I have three notes given by James Appleton; one of $75, payable in 30 days, one of $50, payable in 60 days, and one of $500, payable in 90 days. What is the equated time for the payment of the whole?

2. A merchant sold goods, agreeing to receive of the amount in 3 months, † in 6 months, and the rest in 9 months. At what time might the bill be settled by a single payment?

3. What is the equated time for the payment of $1000, of the sum being now due, in 3 months, and in 9 months? [The $250 now due has no time to run, and the product 250×0=0.]

4. What is the equated time for the payment of a debt, of which is now due, in 3 months, in 9 months, and the remainder in 15 months?

5. What is the equated time for the payment of three debts, one of $100, due in 8mo., one of $25, due in 11y., and one of $90, due in 2y.?

6. On a debt of $400, due in 9mo., a payment of $100 is made in 3mo. In what time should the remainder be

paid?

7. I owe $40, payable now, $40 in 30 days, $20 in 60

days, and $100 in 120 days. What is the equated time for the payment of the whole?

8. Manson & Hill, of Liverpool, have given to Thomas Morton & Co. of New York, a note of £225 10s., payable in 60 days; one of £196, payable in 60 days; one of £218 78. 6d., payable in 90 days; and one of £300, payable in 120 days. At what time may the notes all be cancelled by a single payment?

9. On a debt of £1100, due in 9mo., a payment of £159 4s. is made in 3mo., and another of £300 in 41mo. What is the equated time for the payment of the balance?

By this rule we may obtain the average price of a number of ingredients of different value. The quantity of the several ingredients is substituted for the debts, and the price for the times.

10. A grocer mixes 10 pounds of tea, at 50 cents a pound, 12 pounds at 75 cents, and 16 pounds at 62 cents. What is the value of a pound of the mixture?

11. If 12 gallons of water are mixed with 9 gallons of wine, at $1.00 per gallon, and 12 gallons at $1.50, what is the mixture worth per gallon?

12. Required the average length of 5 pieces of sheet. ing, measuring as follows: No. 1, 321yd.; No. 2, 31 łyd.; No. 3, 331yd.; No. 4, 303yd.; No. 5, 34yd.

13. If I mix 3lb. of gold 22 carats fine, 5lb. 20 carats fine, 8lb. 24 carats fine, 10lb. 23 carats fine, and 2lb. of alloy, what will be the fineness of the mixture? [A carat is 24 Pure gold is 24 carats fine. Alloy is counted of no value.]

14. A grocer mixed 18 gallons of molasses, at 25 cents a gallon, with 20 gallons at 30 cents, 24 gallons at 40 cents, and 5 gallons of water. At what price per gallon must he sell the mixture to gain 25 per cent. ?

15. If the thermometer stands from 6 to 9 at 68°, from 9 to 11 at 70, from 11 to 1 at 73°, from 1 to 4 at 77°, and from 4 to 6 at 76°, what is the average temperature of the 12 hours?

16. The following charges are made against Walton & Morris, each payable in 8 months, viz: Jan. 25, $1643. 50; Feb. 1, $900; Feb. 16, $1131.25; Feb. 28, $241,

75; March 13, $971; and April 3, $763.37. What should be the date of a single note at 8 months, for the whole amount?

17. What must be the date of a note at 6 months, for the amount of the following charges, each payable in 8 months? March 19, $59.63; April 3, $713.20; April 15, $2350; April 21, $1975.37; July 5, $163.25; and Sept. 19, $251.17.

18. What should be the date of a note at 9 months, for the amount of the following charges? May 23, $840 at 6mo.; May 30, $900 at 8mo.; June 15, $325 at 4mo.; June 27, $563.50 at 3mo.; July 13, $729 at 6mo.; and July 16, $421.75 at 9mo.

19. A jeweller mixed 37b. 6oz. silver, 9oz. fine, 4lb. of 11oz. fine, 2īb. 3oz. of 10žoz. fine, and 2lb. of 10oz. fine. What was the fineness of the mixture? [11oz. fine, denotes that 11oz. in the lb. are silver, and the rest alloy. Pure silver is 12oz. fine.]

20. If 17b. silver, 8oz. fine, 2lb. of 9oz. fine, 3lb. of 10oz. fine, 4lb. of 11oz. fine, and 57b. alloy, be melted together, what will be the fineness of the mixture?

21. Marshall & Wood, to George W. Hall,

Dr.

What should be the date of a note at 6mo, for the whole

amount?

22. A farmer mixed 18 bushels of wheat, at $1.00 per bushel; 16 bu. at $1.12 per bushel; 13§bu. of barley, at 62 cts. per bushel, and 10bu. of oats, at 37 cts. per bushel. What was the mixture worth per peck?

23. What should be the date of a note at 60 days (or 63 days, including the days of grace) for $150, due April 7,-$200, due April 13,-$75, due April 17,-$325, due April 29, $180, due April 30,-$400, due May 4,-and $439, due May 11?