7. What principal will, in 43 9. What principal will, in 62 10. What principal will, in 8 amount to $76? years, at 6 per cent., years, at 7 per cent., years, at 7 per cent., years, at 6 per cent., The present worth of a debt payable at some fu ture time, without interest, is such a sum as will, in the given time, and at the given rate per cent., amount to the debt. Hence, the present worth of any sum of money, payable at some future time without interest, may be found in the same way that we found the principal, when the amount, time, and rate per cent. were given. See the Analysis of this Lesson. 11. What is the present worth of $26, due 5 years hence, at 6 per cent.? Ans. $20. 12. What is the present worth of $14, due 8 years hence, at 5 per cent.? 13. What is the present worth of $110, due 5 years hence, at 5 per cent.? 14. What is the present worth of $86, due 8 years hence, at 9 per cent.? 15. What is the present worth of $102, due 9 years hence, at 4 per cent.? 16. What is the present worth of $72, due 4 years hence, at 5 per cent.? Discount equals the amount minus the present worth. 7. What is the discount on $46, due 3 years hence, at 5 per cent.? 18. What is the discount on $54, due 5 years hence, at 7 per cent.? 19. What is the discount on $65, due 5 years hence, at 6 per cent.? 20. What is the discount on $93, due 3 years hence, at 8 per cent.? 21. What is the present worth of $186, due 43 years hence, at 5 per cent.? 22. What is the present worth of $66, due 5 years hence, at 6 per cent.? 23. What is the present worth of $128, due 43 years hence, at 6 per cent.? r. If I sell cloth at $2.50 a yard, and thereby gain 25 per cent., what did it cost a yard? ANALYSIS.-If I gain 25 per cent., I gain of the cost; to which add, the cost, and I have of the cost equal to $2.50. If of the cost is $2.50, of the cost is of $2.50, or 50 cents; and (the cost) is 4 times 50 cents, which are 200 cents, or $2. 2. A horse was sold for $38, which was at a loss of 5%; what did the horse cost? 3. If I sell cloth at $2.50 a yard, and thereby gain 25%, how must I sell it a yard to lose 20% ? 4. If I sell cloth at $4.40 a metre, and thereby gain 10%, how ought I sell it to lose 25% ? 5. If by selling a piece of cloth for $46, I gain 15%, how ought I to have sold it, to have lost 30% ? 6. A. sold his horse for $105, and thereby gained 5%; for what ought he to have sold it, to have lost 10%? 7. A farm was sold for $495, which was 10% less than what it was worth; for what ought it to have been sold, to have received 40% more than its value? 8 A mechanic lost 20% on the cost of a wagon, by selling it for $40; for what ought it to have been sold, to have gained 30 per cent.? 9. A hectare was sold for $90, which was 10% less than its value; what would have been the gain per cent., if it had been sold for $120 ? 10. A farm was sold for $690, which was 8% less than its value; what would have been the gain % on its value, if it had been sold for $850? 11. A book was sold for 90 cents, which was 10% less than its value; what would have been the gain % on its value, if it had been sold for $1.50? 12. A man sold two watches, at $12 each; on one he gained 50%, and on the other he lost 50%. Did he gain or lose by the bargain, and how much? 13. An individual sold two gold pencils, at $6 each; on one he gained 20%, and on the other he lost 20%. Did he gain or lose, and how much? 14. A farmer sold two horses at $210 each; for one he received 25% more than its value, and for the other 25% less than its value. Did he gain or lose by the sale of both, and how much? 15. A merchant sold a quantity of cloth for $280, and by so doing lost 60%; he then sold another quantity for $80, and gained 60%. Did he gain or lose by the entire sale, and how much? LESSON LXXVI. I. An individual was ordered to collect $190, and his own fee, which was to be 5 per cent. on all the money collected. How much should he receive? ANALYSIS.—He is to receive 5 per cent., or 5, or of all he collects., all he collects, minus go, his fee, equals of all he collects, or $190, the amount he is to pay his employer. If of what he collects equals $190, is ' of $190, which is $10; and 28 (what he collects) is 20 times $10, or $200. Therefore he must receive $200-$190=$10. 2. How much ought A. to receive for collecting $90 and his own fee of 10 per cent. on all he collects? 3. What amount of money will be sufficient to pay a debt of $38 and the collector's fee, which is 5 per cent. on all the money collected? 4. How much cider must that man make to bring away 15 barrels, after the owner of the mill receives 163 per cent. of all he has made? 5 How much grain must a farmer take to mill, that he may bring away the flour of 1 bushel, after the miller has taken 10 per cent. of all he took there? MISCELLANEOUS QUESTIONS. 1. At 5 per cent. for 4 years, what part of the principal equals the interest? 2. In how many years, at 4 per cent., will the interest on a given principal amount to the same sum, as it will in 8 years, at 6 per cent.? 3. At what rate per cent. will the interest on a given principal, in 14 years, amount to the same sum, as it will in 12 years at 7 per cent. ? 4. If of the principal equals the interest, what is the rate per cent.? 5. The rent of B.'s farm, for 8 years, equaled 32 of its value; what per cent. did he annually receive on the value of his farm? 6. What is the interest of $75, for 5 years, at 6 per cent.? 7. What principal will, in 7 give $24 interest? 8. What principal will, in 4 amount to $155 ? years, at 8 per cent., years, at 5 per cent., 9 At what rate per cent. will a given principal double itself in 12 years? 10. The interest of A.'s and B.'s fortune, for 8 years, at 5 per cent., is $420; what is the fortune of each, provided A.'s fortune is twice B.'s? II. The interest of of A.'s and of B.'s fortune, for 7 years, at 5 per cent., is $2100; what is each of their fortunes, provided of A.'s fortune equals of B.'s? 12. B. sold his horse for of 13 times what it cost; what did he lose per cent.? 13. What is the interest of $540 for 4 years, at 5 per cent.? 14. What is the interest of $180, for 5 years and 9 months, at 63 per cent.? 15. What principal will in 4 years 7 months and 6 days, at 61 per cent., amount to $412 ? 16. The interest of the cost of B.'s horse, sleigh, and wagon, for 6 for 6 years, at 5 per cent., is $69. What is the cost of each, provided their prices are to each other as, 3, and ? 17. What principal will, in 8 years and 8 months, at 7 per cent., amount to $419? 18. What principal will, in 5 years 9 months and 18 days, at 10 per cent., give $116 interest? 19. In what time will $420, at 5 per cent., give $147 interest ? 20. If the interest of $200, for 1 year and 6 months, is $18, what is the rate per cent.? 21. At what rate per cent., will $500, in 4 years and 9 months, give $190 interest? 22. At what rate per cent., will $500, in 22 years and 6 days, amount to $1821? 23. At what rate per cent. will a given principal double itself, in 20 years? 24. In what time will the amount be double a given principal, at 12 per cent.? 25. At what rate per cent. will the amount be double a given principal, in 6 years and 8 months? 26. A horse was bought for $60, and sold for $90; what was the gain per cent.? |