Multiply the present worth of £1 annuity for the time and rate per cent. given by the annuity, persion, &c. it will give the answer. EXAMPLES. 29. What is the present worth of an annuity of £30 per annum, to continue 7 years, at 6 per cent.? Ans. £167...9...5. 184d. 30 1,50363 19,9517. 10,0483 30-19,9517=10,0483 1,06-1 167,4716. By the table 5,58238 × 30=167,4716. 30. What is the present worth of a pension of £40 per annum, to continue 8 years, at 5 per cent.? 1:3923019498 Ans. £258...10...6 37312859361 31. What is the present worth of a salary of £35, to continue 7 years, at 6 per cent.? Ans. £195...7...8 14423830188 32. What is the yearly rent of £50, to continue 5 years, worth in ready money, at 5 per cent.? 35241334 18bk1° 4084101978. Ans. £216.. 9...5. 2 3591786 II. When P, T, R, are given, to find U. prxr-pri 33. If an annuity be purchased for £167...9...5...184d. to be continued 7 years, at 6 per cent. what is the annuity ? Ans. 167,4716 × 1,50363 × 1,06—167,4716×1,50363 1,50362-1 = £30. 13993019493 34. If the present payment of £258...10...6.37822859381 qrs. be made for a salary 8 years to come, at 5 per cent. what is the salary? Ans. £40. 35. If the present payment of £195...7...8 3524133413531 s. be required for a pension for 7 years to come, at 6 per cent. what is the pension? ̈ 14423830188 Ans. £95. 36. If the present worth of an annuity, 5 years to come, be £216...9...5. 2 404.01 grs. at 5 per cent. what is the annuity? 3594786 37. How long may a lease of £30 yearly rent be had for £167...9...5...184d. allowing 6 per cent. to the purchaser ? visions will be to T1 years. 38. If £258...10...6. 3 13991190 grs. is paid down for a lease of £10 per annum, at 5 per cent. how long is the lease purchased for? 39. If a house is let upon lease for £35 per lessee makes present payment of £195...7...8. allowed 6 per cent. I demand how long the for? Ans. 8 years. annum, and the 14423830188, he being 3523133319511 lease is purchased Ans. 7 years. 3594786 40. For what time may a lease of £50 per annum be purchased, when present payment is made of £216...9...5. 2 4032101 at 5 per cent.? Ans. 5 years. ANNUITIES, LEASES, &c taken in REVERSIÓN. To find the present worth of Annuities, Leases, &c. taken in Reversion. RULE. Find the present worth of the annuity, &c. at the given rate, น and for the time of its continuance; thus, 2. Change Pinto A, and find what principal being put to interest will amount to P at the same rate, and for the time to come, before the annuity commences, which will be the present worth of the annuity, &c. EXAMPLES. a P. 41. What is the present worth of a reversion of a lease of £40 per annum, to continue for 6 years, but not to commence till the end of 2 years, allowing 6 per cent. to the purchaser ? Ans. £175...1...1. 2,048 qrs. 16679888578201 42. What is the present worth of a reversion of a lease of £60 per annum, to continue 7 years, but not to commence till the end of 3 years, allowing 5 per cent. to the purchaser? Ans. £299...18...2:3525415048443 ere is a lease of a house at £30 per annum, which is yet in being for 4 years, and the lessee is desirous to take a lease in reversion for 7 years, to begin when the old lease shall be expired, what will be the present worth of the said lease in reversion, allowing 5 per cent. to the purchaser ? Ans, £142...16 ..341445573652898 To find the Yearly Income of an Annuity, &c. taken in Reversion. RULE. Find the amount of the present worth at the given rate, and for the time before the annuity commences; thus, Change A into P, and find what yearly rent being sold will produce P, at the same rate, and for the time of its continuance, which will. be the yearly sum required EXAMPLES. thus, pr1-A. prt Xr-prt U. 44. What annuity to be entered upon 2 years hence, and then to continue 6 years, may be purchased for £175...1...1. 2,058 grs at 6 per cent. ? 175,0563 × 1,1236=196,6933, then 196,6933 × 1,41852×1,06-279,01337 16679 88097820 1,41852-1 £40 Ans. 45. The present worth of a lease of a house is £299...18...2 3525415948422 d. taken in the reversion for 7 years, but not to commence till the end of 3 years, allowing 5 per cent. to the pur chaser, what is the yearly rent? Ans. £60 46. There is a lease of a house in being for 4 years, and the lessee being minded to take a lease in reversion 7 years, to begin when the old lease shall be expired, paid down £142...16...3. 2176753166847407 95. what was the yearly rent of the house, when the lessee was allowed 5 per cent. for present payment? 41445573652893 Ans. £30. Purchasing FREEHOLD or REAL ESTATES; such as are bought to continue for ever. I. When U, R, are given, to find W. น RULE. ——W. r-] EXAMPLES. 47. What is the worth of a freehold estate of £50 per annum, allowing 5 per cent. to the buyer? 50 Ans. 1,05-1 £1000. 48. What is an estate of £140 per annum, to continue for ever, worth, in present money, allowing 4 per cent. to the buyer? Ans. £3500. 49. If a freehold estate of £75 yearly rent was to be sold, what is the worth, allowing the buyer 6 per cent. II. When W, R, are given, to find U. RULE. WXr1=U. Ans. £1250. EXAMPLES. 50. If a freehold estate is bought for £1000, and the allowance of 5 per cent. is made to the buyer, what is the yearly rent? Ans. 1,05-1=,05, then 1000 ×,05:=£50. 51. If an estate be sold for £3500, and 4 per cent. allowed to the buyer, what is the yearly rent? Ans. £140. 52. If a freehold estate is bought for £1250 present money, and an allowance of 6 per cent. made to the buyer for the same, what is the yearly rent? III. When W, U, are given, to find R. RULE. w+u W R. EXAMPLES. Ans. £75. 53. If an estate of £50 per annum be bought for £1000, what in the rate per cent.? 54. If a freehold estate of £140 per annum be bought for £3500, what is the rate per cent. allowed? Ans. 4 per cent. 55. If an estate of £75 per annum is sold for £1250, what is he rate per cent. allowed? Ans. 6 per cent ་ Purchasing FREEHOLD ESTATE in REVERSION. น RULE. Find the worth of the yearly rent, thus, -————W. Change W into A, and find what principal r—1 being put to interest will amount to A. at the same rate, and for the time to come, before the estate commences, and that will be the worth of a the estate in reversion; EXAMPLES. thus, 56. If. a freehold estate of £50 per annum, to commence 4 years hence, is to be sold, what is it worth, allowing the purchaser 5 per sent. for present payment? Ans. 50 =1000. then- ==£822... 14...1. 2 grs.+ 1,05-1 1000 1,2155 al 57. What is an estate of £200, to continue for ever, but not to commence till the end of 2 years, worth in ready money, lowing the purchaser 4 per cent. ? Ans. £4622...15...7.1 139 58. What is an estate of £210 per annum worth in ready money, to continue for ever, but not to commence till the end of 3 years, allowance being made at 6 per cent. 6974 Ans. £3358...9...6. 214 To And the Yearly Rent of an Estate taken in Reversion. RULE. Find the amount of the worth of the estate, at the given rate and time before it commences? thus, wrt A. Change A into W, and find what yearly rent being sold will produce U, at the wrXr-wr. EXAMPLES. 59. If a freehold estate, to commence 4 years hence, is sold for £822...14...1. 2 qrs. allowing the purchaser 5 per cent. what is the yearly income? Ans. 822,70625 × 1,2155=1000. then 1000 × 1,05 × 1,05—1050 1,05 -=£50. 139 whid 60. A freehold estate is boug t for £4622...15...7. does not commence till the end of 2 years, the buyer being al❤ lowed 4 per cent. for his money; I desire to know the yearly income? Ans. £200. 61. There is a freehold estate sold for £3358...9...6.2 6974 148877 grs. but not to commence till the expiration of 3 years, allowing 6 per cent. for present payment; what is the yearly income? REBATE, OR DISCOUNT. Ans. £240. Table IV. shews the present worth of £1 due any number of years, to commence under 31, rebute at 5 and 6 per cent. NOTE. The above table is thus made, 1÷1,05,952381 first year's present worth; and ,952381-1,05=,90703 second year, and,90703 1,05=,863838 third year, &c. Table continued to 100 years, see page 185 |
