Commutation Tables; For Joint Annuities & Survivorship Assurances, Based on the Carlisle Mortality at 3, 3 12, 4, 5, and 6 Per Cent Interest, with Tables of Annuities & Assurances on Single Lives, and Other Useful Tables, and an (Paperback)

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1858 edition. Excerpt: ... rst Premium ftt the end of each 5 years. 3939 848 3666 272 The first premium is stated by Mr. Jones to be 1:8: 3, which, if increased hy 4s. each 5 years, 273 576 will make the scale too low. Ex. 7. If the scale proposed had been decreas1ng, instead of increasing, all other conditions being the same, i.e., if q had been negative, then the divisor would have been 29314.8901--11421.4659 = 17893.4242 l-t 6 yean. id I years. 3d 5 years. 4th 5 years. Remainder of Life. 2: 19: 1 2:7:4 1: 15: 7 1: 13: 10 0: 12: 1 Ex. 8. Required the annual premium for the first 5 years to insure 100 on a life aged 32, the annual premium to receive an addition of tli part at the end of each of three periods of 5 years, and thereafter to remain constant. Interest at 3 per cent. In this way we may form as many scales as we please, increasing by any other ratio according to the value given to q. From these results, it appears that the greater the value which is given to q, the smaller the first premium necessarily becomes; so that by assuming a high value for q, there is a danger of making the first premium so small that it will be insufficient to cover the risk for the first term. Thus, when q =, the annual premium for the first five years becomes so small, as to be very little more than the annual premium for a five years' insurance, which will be found to be.99229 percent. This should be guarded against. Ex. 9. Required the annual premium for the first five years to insure 100 on a life aged 27, the annual premium to be reduced by th part at the end of each of three periods of five years, and thereafter to remain constant. Interest at 3 per cent. Here the formula is M 3 05947 Hence---=.71487...