called days of grace, and the note is not legally due until the last day of grace. 1. A note for $2000, payable in 30 days, was discounted at a bank. What was received for the note ? 2. What is the bank discount on a note for $1750, payable in 60 days? 3. How much can I obtain by discounting each of the following notes, at 7 per cent. ? $375.50 Providence, Sept. 19, 1844. Ninety days from date, I promise to pay Jacob Murray, or order, three hundred and seventy-five dollars and fifty cents, for value received. MORRIS JOHNSON. $500.00 Hartford, Sept. 3, 1844. Thirty days from date, I promise to pay Evans & Pow. ell, or order, five hundred dollars, for value received. John MILTON. $795,00 Nashville, Aug. 5, 1844. Six months after date, we promise to pay Charles W. Taylor, or order, seven hundred and ninety-five dollars, for value received. EARLE & KING. 4. What are the present worth and the equitable dis. count of $1870, due in 3y. 4mo. 13d.? 5. Wilmington, 5th mo. 7th, 1844. For value received, I promise to pay Jonathan Mason, or order, six hundred and seventy-three dollars and twenty-, five cents, in six months. Moses A. WILSON. $673.25 What ought Moses A. Wilson to pay, in order to cancel the above note, 8th mo. 3d, 1844 ? 6. The Farmers' and Mechanics' Bank offer to discount the following notes at 5 per cent. How much shall I receive on each ? $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. WILLIAM JACOBSON. $144.00 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 received. GEORGE M. WATSON. $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 v 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, 64cwt. of sugar, at 5}cts. a pound ; 81 barrels of flour, at $4.62} per barrel ; 3.679cwt. of coffee, at 8 cts. a pound ; 2cwt. lqr. 17lb. of rice, at $3.50 per cwt. ; 13 boxes sperm candles, each containing 32:16., at 29 cts. per lb.; and 1916. 11oz. chocolate, at 18 cts. 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. Iqr. 171b. of sugar, at $5.00 per cwt. ; 391 3lb. Young Hyson tea, at 87 cts. a pound; 250:16. Imperial tea, at 63 cts. a pound ; 78gal. 3qt. of molasses, at 31 cts, a gallon; and 1273lb. cheese, at 8 cts. 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 fol. lowing amounts ? 1638yd. of silk, at 87 cts. a yard , 491.hyd. India muslins, at 62}cts. a yard ; 363yd. Alpacca, at 93 cts. a yard; 224yd. merino, at 50cts. a yard ; and 251 3yd. printed lawn, at 37 cts, 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 44 per cent. ? 15. What is the value of a note at 90 days, for $4959. 375, discounting at 43 per cent.? 16. What is the value of į of of a note at 120 days, for $7638, discounting at 54 per cent. ? 17. What is the value of 1 of 5 of a note at 30 days, for $10000, discounting at 72 per cent. ? 18. What is the value of sof .97 of g of a note at 4 months, for £2610 78. 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 8 per cent. ? 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 Pax 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 interest? The interest of $4.00 for 3mo.=:The int. of $1.00 for 12mo. The interest of $6.00 for 6mo.=The int. of $1.00 for 36mo. The interest of $2.00 for 12mo.=The int. of $1.00 for 24mo. The interest of $12.00 for —Mo.=The int. of $1.00 for 72mo. He may keep $12.00, 1 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 y 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, 4 of the sum being now due, in 3 months, and į in 9 months ? [The $250 now due has no time to run, and the product 250 x0=0.] 4. What is the equated time for the payment of a debt, 1 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 1 y., 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 7s. 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 4, mo. What is the equated time for the payment of the balance ? By this rule we may obtain the average price of a num. ber 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 62į 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, 32 yd.; No. 2, 31kyd.; * No. 3, 333yd.; No. 4, 30 yd.; No. 5, 34yd. 13. If I mix 3lb. of gold 22 carats fine, 5lb. 20 carats fine, 8lb. 24 carats fine, 101b. 23 carats fine, and 2lb. of alloy, what will be the fineness of the mixture ? [A carat is n'a. 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 g at 68°, from 9 to 11 at 70,o from 11 to 1 at 73°, from 1 to 4 at 77°, and com 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, |