5. What is the interest of $1768, for 11 months 28 days? Ans. $1.054 6. What is the interest of $200 for 1 day? 2 days? 3 days? 4 days? 5 days? Ans. for 5 days, $0'166. 7. What is the interest of half a mill for 567 years? Ans. $0'017. 8. What is the interest of $81, for 2 years 14 days, at per cent. ? per cent.? cent. ? 3 per cent.? eent.? 6 per cent.? cent.? 8 per cent.? cent. ? 12 per cent. ? 9 per cent. ? 10 per 124 per cent. ? Ans. to last, $20'643. 9. What is the interest of 9 cents for 45 years, 7 months, 11 days? Ans. $0'245. 10. A's note of $175 was given Dec. 6, 1798, on which was endorsed one year's interest; what was there due Jan. 1803? 1, Note. Consult ex. 16, Supplement to Subtraction of Compound Numbers. Ans. $207'22. 11. B's note of $56'75 was given June 6, 1801, on interest after 90 days; what was there due Feb. 9, 1802?' Ans. $58'19, 12. C's note of $365'37 was given Dec. 3, 1797; June 7, 1800, he paid $97'16; what was there due Sept. 11, Ans. $328 32. 1800? 13. Supposing a note of $31792, dated July 5, 1797, on which were endorsed the following payments, viz. Sept. 13, 1799, $208'04; March 10, 1800, $76; what was there due Jan. 1, 1801 ? Ans. $83'991. SUPPLEMENT TO INTEREST. QUESTIONS. 1. What is interest? 2. How is it computed? 3. What is understood by rate per cent.? 4. 5. by amount? 6. by commission ? 8. below par? 15. The rate per cent. is a decimal carried to how many places? 16. What are decimal expressions lower than hundredths? 17. How is interest, (when the time is 1 year,) commission, insurance, or any thing else rated at so much per cent. without respect to time, found? 18. When the rate is 1 per cent., or less, how may the operation be contracted? 19. How is the interest on $ 1, at 6 per cent. for any given time, found by inspection? 20. How is interest cast, at 6 per cent., when there are months and days in the given time? 21. When the given time is less than 6 days, how is the interest most readily found? 22. If the sum given be in pounds, shillings, &c., how is interest cast? 23. When the rate is any other than 6 per cent, if there be months and days in the given time, how is the interest found? 24. What is the rule for casting interest on notes, &c. when partial payments have been made, and what is the principle on which the rule is founded? How may the principal be found, the time, rate per cent., and amount being given? 26. What is understood by discount? 27. by present worth? 28. How is the principal found, the time, rate per cent., and interest being given ? 29. How is the rate per cent. of gain or loss found, the prices at which goods are bought and sold being given? 30. How is the rate per cent. found, the principal, interest, and time being given? 31. How is the time found, the principal, rate per cent., and interest being given? 32. What is simple interest? 33. compound interest? 34. How is compound interest computed? EXERCISES. 25. 1. What is the interest of $273'51 for 1 year 10 days, at 7 per cent. ? Ans. 19'677. 2. What is the interest of $486 for 1 year, 3 months, 19 days, at 8 per cent.? Ans. $50'652. 3. D's note of $203'17 was given Oct. 5, 1808, on interest after three months; Jan. 5, 1809, he paid $50; what was there due May 2, 1811? Ans. $174'53. 4. E's note of $870'05 was given Nov. 17, 1800, on interest after 90 days; Feb. 11, 1805, he paid $ 186'06; what was there due Dec. 23, 1807? Ans. $1041'58. 5. What will be the annual insurance, at & per cent, on a house valued at $1600 ? Ans. 10. 6. What will be the insurance of a ship and cargo, valued at $5643, at 14 per cent.? per cent.? at per cent. ? at per cent.? Ans. at at per cent. ? Note. Consult ¶ 82, ex. 11. T 7. A man having compromised with cents on a dollar, what must he pay on at per cent. $42'322 his creditors at 621 a debt of $137'46? Ans. $85'912 8. What is the value of $800 United States Bank stock, Ans. $900. at 1121 per cent. ? 9. What is the value of $560'75 of stock, at 93 per cent.? Ans. $521'497 10. What principal at 7 per cent. will, in 9 months 18 days, amount to $422'40 ? Ans. $400. 11. What is the present worth of $426, payable in 4 years and 12 days, discounting at the rate of 5 per cent.? In large sums, to bring out the cents correctly, it will sometimes be necessary to extend the decimal in the divisor to five places. Ans. $354'506. 12. A merchant purchased goods for $250 ready money, and sold them again for $300, payable in 9 months; what did he gain, discounting at 6 per cent. ? Ans. $37'081. 13. 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. 14. The interest on a certain note, for 1 year 9 months, was $49'875; what was the principal ? Ans. $475. 15. What principal, at 5 per cent., in 16 months 24 days, will gain $35 ? Ans. $500. 16. If I pay $15'50 interest for the use of $500, 9 months and 9 days, what is the rate per cent. ? 17. If I buy candles at $167 per lb., and sell them at 20 cents, what shall I gain in laying out $100 ? Ans. $19'76. 13. Bought hats at 4 s. apiece, and sold them again at 4 s. 9 d.; what is the profit in laying out 100 £.? Ans. 18 £. 15s. 19. Bought 37 gallons of brandy, at $1'10 per gallon, and sold it for $40; what was gained or lost per cent. ? 20. At 4 s. 6 d. profit on 1 £., how much is gained in laying out 100 £., that is, how much per cent.? Ans. 22 £. 10 s. 21. Bought cloth at $4'18 per yard; how must I sell it to gain 12 per cent. ? Ans. $5'04. 22. Bought a barrel of powder for 4 £.; for how much must it be sold to lose 10 per cent. ? Ans. 3 £. 12 s · 23. Bought cloth at 15 s. per yard, which not proving so good as I expected, I am content to lose '17 must I sell it per yard? per cent.; how Ans. 12 s. 4 d. 24. Bought 50 gallons of brandy, at 92 cents per gallon, but by accident 10 gallons leaked out; at what rate must I sell the remainder per gallon to gain upon the whole cost at the rate of 10 per cent.? Ans. $1'265 per gallon. 25. 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 lb. to gain 20 per cent. by it? Ans. 6 cents per lb. ¶ 92. Equation of payments is the method of finding the mean time for the payment of several debts, due at different times. 1. In how many months will $1 gain as much as 5 dollars will gain in 6 months? 2. In how many months will $1 gain as much as $40 will gain in 15 months? Ans. 600: 3. In how many months will the use of $5 be worth as much as the use of $1 for 40 months? 4. Borrowed of a friend $1 for 20 months; afterwards lent my friend $4; how long ought he to keep it to become indemnified for the use of the $1? 5. I have three notes against a man; one of $12, due in 3 months; one of $9, due in 5 months; and the other of $6, due in 10 months; the man wishes to pay the whole at once; in what time ought he to pay it? $12 for 3 months is the same as $1 for 36 months, and $9 for 5 months is the same as $1 for 45 months, and $6 for 10 months is the same as $1 for 60 months. 27 141 He might, therefore, have $1 141 months, and he may keep 27 dollars part as long; that is, 45 months 6+days, Answer. T 93. RATIO; OR THE RELATION OF NUMBERS. 1 177 Hence, To find the mean time for several payments,-RULE: -Multiply each sum by its time of payment, and divide the sum of the products by the sum of the payments, and the quotient will be the answer. Note. This rule is founded on the supposition, that what is gained by keeping a debt a certain time after it is due, is the same as what is lost by paying it an equal time before it is due; but, in the first case, the gain is evidently equal to the interest on the debt for the given time, while, in the second case, the loss is only equal to the discount of the debt for that time, which is always less than the interest; therefore, the rule is not exactly true. The error, however, is so trifling, in most questions that occur in business, as scarce to merit notice. 6. A merchant has owing him $300, to be paid as follows: $50 in 2 months, $100 in 5 months, and the rest in 8 months; and it is agreed to make one payment of the whole in what time ought that payment to be? Ans. 6 months. 7. A owes B $136, to be paid in 10 months; $96, to be paid in 7 months; and $260, to be paid in 4 months: what is the equated time for the payment of the whole? Ans. 6 months, 7 days +. 8. A owes B $600, of which $200 is to be paid at the present time, 200 in 4 months, and 200 in 8 months; what is the equated time for the payment of the whole? Ans. 4 months. 9. A owes B $300, to be paid as follows: in 3 months, in 4 months, and the rest in 6 months: what is the equated time? Ans. 4 months. RATIO; OR THE RELATION OF NUMBERS. T 93. 1. What part of 1 gallon is 3 quarts? 1 gallon is 4 quarts, and 3 quarts is of 4 quarts. Ans. of a gallon. 2. What part of 3 quarts is 1 gallon? 1 gallon, being 4 quarts, is of 3 quarts; that is, 4 quarts is 1 time 3 quarts and of another time. Ans. 1. = |