13. If no interest is paid on this note till the principal is due, and if no renewal of the note is made, what will be the amount of the note at the time of payment? 14. If the note is renewed each year, what will be the principal of the note, for the second year? 15. What will be the principal of the note for the third year? 16. What will be the principal of the note for the fourth year? 17. What will be the amount of the last note at the time of payment? 18. How much would the holder, John Foss, lose, by neglecting to obtain any annual payment of interest, or any renewal of the above note? SECTION XXX. DISCOUNT. [See Section XIV. Part I.] Examples. 1. What is the present worth of $475.50, payable in 3 months? 2. What is the present worth of $341.00, payable in 65 days? 3. Present worth of $940.25, payable in 4 months? SECTION XXXI. BANKING. [See Section XIV. Part I.] To find the present worth of a note given to a bank, payable at some future time, find the present worth of 1 dollar for the given time, and multiply the sum named in the note by it. 1. What is the present worth of a note for 100 dollars, discounted at a bank, for 60 days? Interest of 1 dollar for 63 days is .0105; this subtracted from 1 dollar, leaves for the present worth .9895. 2. What is the present worth of a note for $450.00, discounted at a Bank, for 90 days? 3. I give my note to a bank for $250.00, for 60 days; what do I receive? 4. I give my note to a bank for $520.00, for 120 days; what do I receive? 5. Present worth of a bank note for $600.00, discounted for 60 days? 6. Present worth of a bank note for $150.00, discounted for 120 days? 7. Present worth of a bank note for $75,00, discounted for 30 days? 8. Present worth of a bank note for $1000.00, discounted for 60 days? 9. Present worth of a bank note for $560,00, discounted for 120 days? 10. Present worth of a bank note for $150.00, discounted for 30 days? To find what must be the face of a note given to a bank, in order to obtain a certain sum -find the present worth of 1 dollar for the given time, and divide the sum you wish to obtain by it; the quotient will express the sum that must be named in the note. This, you observe, is just the reverse of the preceding case. 11. For what sum must I give my note to a bank, payable in 60 days, in order to receive $98.95 ? 12. For what sum must I give my note to a bank, payable in 120 days, in order to receive $509.34? 13. For what sum must I give my note to a bank, payable in 60 days, in order to receive $593.70? 14. For what sum must I give my note to a bank, payable in 30 days, in order to receive $10000.00? 1. A man bought a horse for 75 dollars, and sold him for $82.50; what did he gain per cent.? 2. A man bought a chaise for $178.00, and sold it for $154.50; what did he lose per cent.? 3. A merchant bought a lot of flour at $4.62 a barrel, and sold it at $5.15 a barrel; what was his gain per cent.? 4. A merchant bought a piece of broadcloth for $4.30 per yard; what must he sell it for to gain 12 per cent.? 5. A man has $1200.00 invested in a manufactory; he receives, for his half-yearly dividend, 30 dollars; what per cent. is that on his stock? 6. A merchant fails, owing $8540.00, and can pay but $2700.00; how much will that be on a dollar? 7. A man failing in business, agrees to pay his creditors 87 cents on a dollar; what must a creditor receive, whose claim is $740.30 ? The pupil should be encouraged habitually to reason upon the operations he performs; so that his method of procedure may be suggested by the relations of the numbers, and not dictated by a special rule. To aid in this important habit, a few remarks will be made on some of the foregoing examples. These may serve as specimens of analysis, and suggest to the student a similar course of reasoning in other cases. Example 1. The whole gain is $7.50; if this gain were made on an outlay of one dollar, the gain would be seven hundred and fifty per cent.; but the gain is made on an outlay of 75 dollars; the gain per cent., therefore, is one seventy-fifth of the whole gain. Example 4. If the cost was 1 dollar a yard, he must add 12 cents; if 2 dollars, he must add 24 cents, &c. Example 5. If 30 dollars had been the gain upon 1 dollar, it would have been 30 hundred per cent.; but the gain was upon 1200 dollars; the per cent., therefore, must be one twelve hundredth of 30 dollars. 8. I invest in a factory 1260 dollars, and receive for my yearly dividend 86 dollars; what is that per cent.? 9. I purchase flour at $4.75 per barrel; what must I sell it for to gain 12 per cent.? 10. A merchant bought a ship for 11475 dollars, and sold her for $13680; what did he gain per cent.? 11. The population of the State of New York in 1810, was 959949; in 1820, it was 1372812; what was the gain per cent. in that term of 10 years? 12. In 1830, it was 1918604; what was the gain per cent. from 1820 to 1830? 13. In 1840, it was 2428921; what was the gain per cent. from 1830 to 1840? 14. The population of Ohio in 1810, was 230760; in 1820, it was 581434; what was the gain per cent.? 15. The population of Ohio in 1830, was 937903; what was the gain per cent. from 1820 to 1830? 16. In 1840, it was 1519467; what was the gain per cent. from 1830 to 1840? 17. Massachusetts had, in 1810, 472040 inhabitants; in 1820, it had 523287; what was the gain per cent. in 10 years? 18. Massachusetts had, in 1830, 610408 inhabitants; what was her gain per cent. from 1820 to 1830? 19. In 1840, Massachusetts had 737699 inhabitants; what was the gain per cent. from 1830 to 1840? 20. An agent sells 12000 dollars' worth of cloth for a factory, charging 2 per cent. commission; what will be his remuneration? 21. If I buy for a merchant, at a commission of 4 per cent., 500 barrels of flour, at $4.40 per barrel, what am I entitled to for my commission? 22. What is 3 per cent. on $674.54? 23. What is 2 per cent. on $781.50? 24. What is the value of five 100 dollar shares in a bank, at 41 per cent. advance? 25. What is the value of seven 100 dollar shares, at 6 per cent. discount? 26. What is the value of 18 shares bank stock, 60 dollars a share, at 4 per cent. discount? 27. What is the duty on a quantity of broadcloth, whose value is 1735 dollars, at 15 per cent.? 28. What is the duty on a quantity of iron, whose value is 3456 dollars, at 18 per cent.? 29. What is the commission on the sale of 1246 dollars' worth of cloth, at 3 per cent.? 30. A man bought a lot of hay for 13 dollars a ton; he sold it for $14.25 a ton; what did he gain per cent.? 31. Bought tea for 46 cents a pound; what must I sell it for a pound to gain 12 per cent.? 32. What is the worth of 750 dollars, bank stock, at 7 per cent. advance? 33. What is the worth of 8500 dollars, bank stock, at 9 cent. discount? per 34. I sell flour at $5.32 per barrel, and thereby gain 12 per cent. on my outlay, what did the flour cost? Every $1.00 laid out in the purchase has brought me a return of $1.12; the number of dollars I paid out on a barrel must therefore equal the number of times $1.12 will go in $5.32. 35. A merchant sells a ship for 13680 dollars, gaining thereby 14 per cent. on what she cost him; what did the ship cost? 36. 300 dollars is 24 per cent. on what sum? 37. $15.63 is 2 per cent. on what sum? 38. Bought 12 barrels of flour, each containing 196 pounds, at $5.42 per barrel, and sold it at 26 cents for 7 pounds; how much gain in the whole, and how much gain per cent.? 39. Bought 43 dozen pairs of shoes, at $4.30 per dozen, and sold them at 62 cents per pair; what gain in all? what gain per cent.? 40. Bought 20 barrels of apples, each containing 23 bushels, at $2.10 per barrel, and sold them at $1.25 per bushel; What gain in all? what gain per cent.? 41. Bought 375 barrels of flour, at $5.20 per barrel, and sold 200 barrels at $6.10, the remainder at $6.42 per barrel; What gain in all? what gain per cent.? 42. Bought 34 acres of land, at 41 dollars per acre; sold it for $1700.00; how much gain in all? what gain per cent.? |