EXAMPLES. 15. What principal, being put to interest, will amount to £367...13...5. 3,04 grs. in 7 years, at 41 per cent. per annum & Ans ,045 X 7+1=1,315, then 367,674 1,315=£279...12...0. 16. What principal, being put to interest, will amount to £376...19...11. 2,8 in 5 years, at 3 per cent. per annum? Ans. £320...17...0. 17. What principal, being put to interest, will amount to £1130...9...0.1,92 grs. in 5 years, at 4 per cent. per annum ? Ans. £926...12...0. 18. What principal will amouut to £310...14...1,35080061 grs. in 4 years, 175 days, at 3 per cent. per annum? IV. When A, P, T, are given to find R. Ans. £273...18...0. 19. At what rate per cent. will £279 .12...0 amount to £367...13...5. 3,04 qrs. in 7 years? Ans. 367,674-279,6—88,074, 279,6×7=1957,2, then 88,074 1957,2,045, or 41 per cent. 20. At what rate per cent. will £320...17...0 amount to £376...19...11, 2,8 grs. in 5 years? 21. At what rate per cent, will £1130...9...0. 1,92 qrs. in 5 years 22. At what rate per cent. will £310...14...1,35080064 qrs. in 4 years, 175 days? ? Ans, 3 per cent. £926...12...0. amount to Ans. 4 per cent. £273...18...0 amount to V. When A, P, R, are given, to find T. Ans. 3 per cent. 23. In what time will £272...12...0 amount to £367... 13...5. 3,04 grs. at 4 per cent.? Ans. 367,674-279,6—88,074. ·| 279,6X,045 12,5820, then 88,074-12,5820 24. In what time will £320...17...0 amount to £276...19...11. 2,8 grs. at 31 per cent.? Ans. 5 years. 7 years. 25. In what time will £926 1...0 amount to £1130...9...0, 1,9% qrs. at 4 per cent.? Ans. 5 years 26. In what time will £273...18...0 amount to £310...14...11 ,35080064 qrs. at 3 per cent.? Ans. 4 years, 175 days. ANNUITIES, OR PENSIONS, &c. IN ARREARS Annuities, or Pensions, &c. are said to be in arrears, when they are payable or due, either yearly, half-yearly, or quarterly, and are unpaid for any number of payments. NOTE. U represents the annuity, pension, or yearly rent, T, R, A, as before. I. When U, R, T, are given to find A. 27. If a salary of £150 be forborne 5 years, at 5 per cent. what would it amount to? Ans. £825. 3000 5X5X150-5X150-3000 then −×,05+5×150=£825. 2 28. If £250 yearly pension be forborne 7 years, what will it mount to in that time at 6 per cent.? Ans. £2065. 29. There is a house let upon lease for 5 years at £60. per annum what will be the amount of the whole time, at 44 per cent.? Ans. £363...8...3. 30. Suppose an annual pension of £28 remain unpaid for 8 years, what would it amount to at 5 per cent. ? Ans. £263...4...0. Note. When the annuities, &c. are to be paid half-yearly, or quarterly, then For half yearly payment, take half of the ratio, half of the annuity, &c. and twice the number of years,—and, For quarterly payments, luke a fourth part of the ratio, a fourth part of the annuity. &c. and four times the number of years, and work us before. EXAMPLES. 31. If a salary of £150 payable every half-year, remains unpaid for 5 years, what would it amount to in that time at 5 per cent.? Ans. £834...7...6. 32. If a salary of £150 payable every quarter, was left unpaid for 5 years, what would it amount to in that time at 5 per cent.? Ans. £839...1...3. Note. It may be observed by comparing these last examples, the amount of the half-yearly payments are more advantageous than the yearly, and the quarterly more than the half-yearly. II. When A, R, T, are given to find Ư. 33. If a salary amounted to £825 in five years, at 5 per cent. what was the salary? Ans. £150. 825X2=1650,5 × 5 ×,05—5 ×,05+5×2—11 then 1656-11 =£150. 34. If a house is to be let upon a lease for 5 years, and N the amount for that time be £363.. 8...3, at 41 per cent. what is the yearly rent? Ans. £60. 85. If a pension amounted to £2065 in 7 years, at 6 per cent. what is the pension ? Ans. £250. 36. Suppose the amount of a pension be £963...4...0 in 8 years, at 5 per cent. what is the pension? Ans. £28. Note. When the payments are half-yearly, then take 4a and half of the ratio, and twice the number of years: and if quarterly, then take 8a, one fourth of the ratio, and four times the number of years, and proceed as before. 37. If the amount of a salary, payable half yearly, for 5 years, and at 5 per cent. be £834...7...6, what is the salary? Ans £150, 38. If the amount of an annuity, payable quarterly, be £839 1...3 for 5 years, at 5 per cent. what is the annuity ? Ans. £150. III. When U, A, T, are given to find R. RULE. 2a-2ut utt-ut R. EXAMPLES. 39. If a salary of £150 per annum amount to £825 in 5 years, what is the rate per cent.? 825×2-150×5×2=150, then Ans. 5 per cent.. 150 -=,05 150 × 5 × 5-150X5 40. If a house be let upon lease for 5 years, at £60, per annum, and the amount for that time be £363...8...3 what is the rate per cent. ? Ans. 41 per cent. 41. If a pension of £250 per annum amounts to £2065 in 7 years, what is the rate per cent. ? Ans. 6 per cent. 42. Suppose the amount of a yearly pension of £28. be £268 4...0 in 8 years, what is the rate per cent.? Ans. 5 per cent. Note. When the payments are half-yearly, take 4a-4ut for a dividend, and work with half the annuity, and double the number of years for a divisor; if quarterly, tuke 8a-8ut, and work with a fourth of the annuity, and four times the number of years. 43. If a salary of £150 per annum, payable half-yearly, amounts to £834...7...6 in 5 years, what is the rate per cent.? Ans. 5 per cent. 44. If an annuity of £150 per annum, payable quarterly, amounts to £839...1...3 in years, what is the rate per cent. ? Ans. 5 per cent. IV. When U, A, R, are given to find T. EXAMPLES. 45. In what time will a salary of £150 per annum amount to £825 at 5 per cent.? 46. If a house is let upon lease for a certain time for £60 per annum, and the amount to £363...S...3, at 4 per cent. what time was it let for? Ans. 5 years. 47. If a pension of £250 per annum, being forborne a certain time amounts to £2065, at 6 per cent. what was bearance ? the time of forAns. 7 years. £28 amount to Ans. 8 years. 48. In what time will a yearly pension of 263...4-..0, at 5 per cent.? Note. If the payments are half-yearly, take half the ratio and half the annuity; if quarterly, one fourth of the ratio and one fourth of the annuity; and T will be equal to those half-yearly or quarterly payments. 49. If an annuity of £150 per annum, payable half-yearly, amounts to £834...7...6, at 5 per cent. what time was the payment forborne ? Ans. 5 years. 50. If a yearly pension of £15), pavable quarterly, amounts *o £839...1...3, at 5 per cent. what was the time of forbearance? Ans. 5 years, PRESENT WORTH OF ANNUITIES. Note. P represents the present worth; U, T, R, as before. 1. When U, T, R, are given, to find P. EXAMPLES. 51. What is the present worth of £150 per annum, to continue 5 years at 5 per cent.? Ans. £660. 5x5x,05-5 ×,05 +5 × 2=11, 5 ׂ05 × 2+2=2,5 52. What is the yearly rent of a house of £60, to continue years, worth in ready money, at 44 per cent.? Ans. £291...6...3 53. What is the present worth of £250 per annum, to continue 7 years, at 6 per cent.? Ans. £1454.4 ..68. 54. What is a pension of £23 per annum, worth in ready money, at 5 per cent. for 8 years? Ans. £188. Note. The same thing is to be observed as in the first rule of an muitics in arrears, concerning half-yearly and quarterly payments. 55. What is the present worth of £150, payable quarterly, for years, at 5 per cent.? Ans. £671...5...0. Note. By comparing the last examples it will be found that the present worth of half-yearly payments is more advantageous than ycarly : and quarterly than half-yearly. II. When P, T, R, are given, to find U. 56. If the present worth of a salary be £660, to continue & years at 5 per cent. what was the salary? 5X,05+1=1,25 Ans. £150. 5X5X,05-5x,05+10=11. 11 1,25 57. There is a house let upon lease for 5 years to come, I desire to know the yearly rent, when the present worth at 41 per cent. is £291...6...315 མ་་་ Ans. £60. 58. What annuity is that which for 7 years continuance, at 6 per cent. produces, £1454...4...6 present worth? Ans. £250. 59. What annuity is that which for 8 years continuance produces £188 for the present worth, at 5 per cent.? Ans. £28. Note. When the payments are half-yearly, take half the ratio, twice the number of years, and multiply by 4p, and when quarterly. take one fourth of the ratio, four times the number of years, and multiply by 8p. 1 60. There is an annuity payable half-yearly, for 5 years to come, what is the yearly rent, when the present worth, at 5 per cent. is £667...10...0? Ans. £150. 61. There is an annuity payable quarterly, for 5 years to come, I desire to know the yearly income, when the present worth, at 5 per cent. is £671...5...0? Ans, £150. III. When U, P, T, are given, to find R. 62. At what rate per cent. will an annuity of £150 per annum. to continue 5 years, produce the present worth of £660 ? Ans. 5 per cent 150×5-660 × 2=180,2 × 660×5+150×5—150 × 5 × 5—3600 then 180-3600=,05=5 per cent. 63. If a yearly rent of £60 per annum, to continue 5 years, produce £291...6...315, for the present worth, what is the rate per cent.? Ans. 41 per cent |