NOTE. The rule in New-York is somewhat more complex, but it amounts in the end to the same result, or very nearly. 1. For value received I promise to pay ALVAN STEWART, or order, nine hundred ninety-nine dollars ninety-nine cents and nine mills, with interest. New-York, April 1, 1823. $999.999. On this note were the following endorsments: SAMUEL REED. March 1, 1825, $16.666 July 17, 1826, Aug. 5, 1827, $333.333 In finding the times for computing interest, see Art. 107. Dec. 29, 1827, $621.000 What was due Jan. 19, 1828? The first principal on interest from April 1, 1823, $999.999 31.694 Payment, Sept. 14, exceeding interest then due, 166.666 Remainder for a new principal, (Sept. 14, 1823,). Payment, March 1, 1825, less than interest then due, $16.666 Remainder for a new principal, (Aug. 5, 1827,) $700.675 19.618 Payment, Dec. 29, 1827, exceeding interest then due, 621.000 $99.293 .386 Remainder for a new principal, (Dec. 29, 1827,) 2. For value received I promise to pay PETER PARLEY, or order, eight hundred eighty-eight dollars eighty-eight cents and eight mills, with interest. New-York, Jan. 17, 1820. $888.888. On this note were the following endorsements: COMPOUND INTEREST. 206. COMPOUND INTEREST is that which arises from the It is computed by adding the interest to the principal at the end of each year, and making the AMOUNT the principal for the ensuing year. 1. What is the compound interest of $275 for 3 years, at 6 per cent.? $275 given sum, or first principal. .06 $275.... first principal subtracted. Ans. $ 52.529 compound interest for 3 years. 2. What is the amount of $1, at 6 per cent., for 2 years? for 4 years? for 8 years? for 3 years? for 5 years? for 6 years? -for 7 years? Ans. to last, $1.5938+ The amount of $2, for any given time, will be twice as much as the amount of $1; the amount of $3, will be three times as much, &c. Hence, we may form the amounts of $1, for several years, into a table of multipliers for finding the amount of any sum for the same time. TABLE, Showing the amount of £1 or $1, &c. for any number of years, not exceeding 24, at the rates of 5 and 6 per cent. compound interest. Years.15 per cent.16 per cent. Years. 15 per cent.16 per cent. 1.05 2345 CO 1.1025 1.06 13 1.88564 2.13292 1.34009 1.41851 18 2.40661 1.40710 1.50363 19 2.52695 3.02559 8 1.47745 1.59384 20 2.65329 2.85433 3.20713 11 1.71033 1.89829 23 3.07152 3.81974 12 1.79585 2.01219 24 3.22509 4.04893 If any principal be multiplied by the amount of $1, &c., as found above, it will evidently give the AMOUNT of that principal. 3. What is the amount, compound interest, of $500 for 3 years, at 5, and at 6 per cent. ? Ans. $578.81 at 5, and $595.505 at 6 per cent.? 4. What is the amount of $629 for 7 years at 5 per cent. compound in terest? Ans. $885.0659. 5. What is the compound interest of $1256 for 15 years, at 6 per cent.? Ans. $1754.0668. 6. What is the amount, compound interest, of £999 19s. 11d. for 19 years, at 5 per cent.? Ans. £2526 18s. Ild. 1.4730499952qrs. THEORETICAL QUESTIONS. amount? By what rule do you for any number of years? How do What is interest? How is it computed? What is rate per cent.? What does PER CENT. signify? What is principal? find the interest of any sum for 1 year? you find the interest, at 6 per cent., for any given time; that is for any number of years, months, and days? How, at 7 per cent.? How, at any OTHER RATE? How do you find the interest of any sum in pounds, &c. The time, rate per cent, and amount being given, how do you find the principal? Having the prices at which goods are sold, and the gain or loss per cent., how do yound the prime cost?* What is discount? present worth? the RULE? (See Rule, Art. 190.) The time, rate per cent., and interest being given, how do you find the principal? Having the gain or loss of goods, and the gain or loss per cent. how do you find the prime cost? (The same rule as before, only in different language.) The principal, interest, and time being given, how do you find the rate per cent.? The prices at which goods are bought and sold being given, how do you find the GAIN OF LOSS per cent.? The principal, rate per cent., and interest being given, how do you find the time? How do you calculate commission, insurance, buying and selling stock, loss and gain, or any thing else rated at so much per cent. without regard to time? What INSURANCE? -premium? policy? is COMMISSION? STOCK? What can you say with regard to the value of stock? When is it at par? above par? - below par? What can you say of LOSS AND GAIN? What is the rule for computing interest on notes, bonds, &c., when partial payments have been made? What is the principle on which the rule is founded? What is compound interest? How it computed? EXAMPLES FOR PRACTICE. 1. What is the interest of $273.51 for 1 year 10 days, at 7 per cent.? Ans. $19.677 15 2. What is the interest of $399.999 for 2 years, 9 months, and 19 days, at 8 per cent.? Ans. $89.688666 3. D's note of $333.17 was given Oct. 5, 1808, on interest after three months; Jan. 17, 1809, he paid $58; what was there due May 1, 1813? + Ans. $346.818284823 4. E's note of $777.777 was given Nov. 7, 1807, on interest after 90 days; Feb. 27,1817, he paid $133.333; what was there due Dee. 17, 1827? Ans. $1571.29425 5. What will be the insurance of a ship and cargo, valued at $9693, at I per cent.? at per cent.? at per cent.? at 3 per cent. Ans. to last, $7269.75 6. What is the value of $700 United States Bank stock, at 1121 per cent.? Ans. $787.50 7. What principal will, in 9 months 18 days, at 7 per cent., amount to $542.7835? 8. What is the value of $560.75 stock, at 93 per cent.? 9. A man compromised with his creditors at 62 what then must hê pay on a debt of $555.46? Ans. $514. Ans. 521.497. cents on a dollar; Ans. $347.1615. *Let the learner give the process in his own language, as exhibited ander Art. 191, tInterest at 6 per cent. 10. Bought a house and lot for $5000, payable in 9 months, which I sold again for $5500, payable in 15 months; what did I gain on a hundred, the usual rate being 6 per cent. ? Ans. $1.65795. 11. Sold goods for $3120, to be paid, one half in 3 months, and the other half in 6 months; what must be discounted for present payment? Ans. $68.492. 12. The interest on a certain note, for one year 9 months, was $49.875 what was the principal? Ans. $475. 13. Bought 21 barrels of tobacco, weighing 3458lbs., at $9.25 for 100lbs. ready money, and sold it again at $11.871 per hundred on 4 months credit; what did I gain per cent.? Ans. $60.861 14. A merchant bought 10 tons of iron for $950; the freight and duties came to $145, and his own charges to $25, how must he sell it per pound to gain 20 per cent.? Ans. 6 cents. 15. Bought cloth at 15s. per yard, which not proving so good as I expected, I am content to lose 171 per cent.; how must I sell it per yard? Ans. 128. 44d. 16. A stationer sold quills at 8s. 9d. per hundred, by which he gained of his money, he afterwards found them to be in great demand and raised them to 9s. 6d. per hundred; what did he gain per cent. by the latter price? Ans. £26 13s. 4d. 17. Bought a pipe of wine containing 126 gallons at 10s. per gallon, but by accident 16 gallons leaked out; at what rate must I sell the remainder per gallon, to gain upon the whole 124 per cent.? Ans. 12s. 107d. 18. Suppose I receive from Richmond, Virginia, 12 hogsheads of tobacco, weighing 15457lbs., which, with the charges there, amounted to $796.85; freight from thence to New-York $6 per hogshead, cartage and storage there 90 cents per hogshead, and freight to Albany $1.50 per hogshead; what does it stand me in per hundred, and what will be my gain per cent. by selling it at 74 cents a pound on 5 months credit? It stands me in $5.8011449 per h. EQUATION OF PAYMENTS. 207. Equation of payments is a method of finding the mean time for the payment of several sums, due at different times. I. Suppose I have two notes against a man; one of $6, due in 2 months, the other of $4, due in 5 months; and he wishes to pay both of them at one time; what time ought he to have? $6 for 2 months is the same as $1 for 12 months, & $4 for 5 months is the same as $1 for 20 months. Hence it is obvious, that he may keep one dollar 32 months; consequently he may keep 10 dollars part of the time. part of 32 is (32 ÷ 10=) 3mo. 6d., Answer. Hence, 208. To find the mean time of several payments, we have this RULE. Multiply each sum by its TIME of payment, and divide the sum of the PRODUCTS by the sum of the PAYMENTS. The rule is founded on the supposition that what is gained by keeping a debt a certain time after it is due, is equal to what is lost by paying a certain time be fore it is due; but, in the first case, the gain is equal to the interest of the debt for the given time, and in the second, the loss is only equal to the discount of it for the same time; which is always LESS than the interest. The rule, therefore is not exactly true; but the errour is too small to be regarded in business. 2. A owes B $200, of which $40 is to be paid in 3 months, $60 in 5 months, and the remainder in 10 months; what is the equated time for the payment of the whole ? Ans. 7mo. 3d. 3. A man bought a quantity of goods, for which he is to pay part 纛 cash, in 3 months, and the remaining in 8 months; but it was afterwards agreed to pay the whole at one equated time; required that time? Ans. 4 months. 4. Cowes D $1400, to be paid in 3 months, but D being in want of money, C pays him at the expiration of 2 months, $1000; how much longer than 3 months ought C, in equity, to defer the payment of the rest? Ans. 2 months. 5. Peter is indebted to William $164.166, of which is to be paid in 6 months, in 8 months, and in 12 months; I demand the equated time for the payment of the whole? Ans. 7 months. THEORETICAL QUESTIONS.-What is equation of payments? What the RULE ? Upon what is the rule founded? Wherein is it not exactly true? FELLOWSHIP. 209. Fellowship is a method of ascertaining the respective gains or losses of individuals, engaged in joint trade. 210. The money, or value of the articles employed, is called the Capital or Stock; the gain or loss to be shared is called the Dividend. Two men bought goods; A paid $60, and B $40; in the sale of them they lose $20; what share of the loss must each man sustain ? 211. It is evident that each man's gain or loss ought to have the same ratio to the whole gain or loss, as his share of the stock to the whole stock, Hence we have this RULE. As the WHOLE Stock: is to each man's SHARE of the stock: so is the WHOLE gain or loss: to his share of the gain or loss. 2. Two men are partners in trade; A put in $350, and B $450; they gain $500; what is each man's share of the gain? The whole stock is 350+ 450 = $800; Then Each man's share of gain. $218.75 A's gain. : : $500 : {$281.25 B's gain. Proof $500.00 whole gain. 3. Two boys, Charles and Henry, bought a lottery ticket; Charles paid $1.50, and Henry $2; the ticket drew a $20 prize; how much of it is each one to receive? Ans. Charles $8.571, and Henry $11.429. 4. Two persons have a joint stock of $1000; whereof A put in $450, and B 550; by ill luck they lose $350: what share of the loss must each sustain ? Ans. A's $157.50. B's 192.50. 5. A, B and C bought a ticket for $3; A paid $ .90, B $1, and C the remainder; the ticket drew a prize of $2000, subject to a deduction of 121⁄2 per cent.; how much is each to receive? Ans. A $525, B $583.3331, and C $641.6663. 6. Three men trade in company; A's capital was $275, B's $300, and |