# Graduated Exercises and Examples for the Use of Students of the Institute of Actuaries' Text-book: Pt. I. Interest (including Annuities - Certain). Pt. II. Life Contingencies ( Including Life Annuities and Assurances). with Solutions

C. and E. Layton, 1889 - Annuities - 120 pages

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Page 23 - ... years, is found by the table to be \$0.34060, and such value of \$50,000 would be fifty thousand times as much, or \$17,030, the amount upon which tax accrues.
Page 23 - A is to enjoy the whole annuity during his life ; but after his decease it is to be divided equally between B and C during their joint lives ; and the survivor of them is to have the whole : To find the value of their respective shares.
Page 99 - ... against (y), by modifying these symbols in the manner just shown, we acquire the means of indicating the values of the several benefits under the variety of circumstances to which they are respectively subject. 193. We now proceed to the LEMMA. If B denote the present value of a benefit of £1. upon a given life or combination of lives, and such that, in the case of a combination of lives the risk is determined by the failure of any one of them ; and if...
Page 2 - A gives B a bill for \$a, due at the end of m years, in discharge of a bill for \$b, due at the end of n years: for what sum should B give A a bill due at the end of p years, to balance the account at...
Page 70 - ... cost of money will be the interest rate in effect each month. (Under this method, the cost of money is determined monthly and the total for the cost accounting period is the sum of the monthly amounts.) (b) The imputed cost of money will be capitalized only once in any cost accounting period, either at the end of the period or at the end of the construction, fabrication, or development period, whichever comes first. (c) When the construction of an asset takes more than one cost accounting period,...
Page 100 - TT denote the probability of a payment of B being received in the first year, and II the probability of the single life, or of all the lives, on which that benefit depends, surviving a year ; — then will the following equation always subsist : — For, if the benefit...
Page 26 - ... 61, 50, and 45, each renewable at the end of the year in which it drops by a life of 7 years of age on payment of a fine of £5. Give an expression for the present value of all the fines for ever.
Page 26 - Give an expression for the present value of all the fines for ever. (164).—A perpetual annuity is to be enjoyed, first by a person aged x for his life, afterwards by a successor to be appointed at his death, and when the second life fails, by a third to be then appointed, and so on. Determine the present value of the annuity for the first n successive lives, the ages being all different.
Page 9 - How to value leaseholds. — Divide the proposed purchase money by the number of years to run before the lease expires ; the quotient, deducted from the net rental, gives the interest on the purchase money. Is this correct ? If not, show how the true rate of interest is to be found. 5. Having given a complete table of px, accurately representing the probabilities of life at all ages, show how, from the deaths taking place in one year, to calculate approximately the total numbers living in a stationary...
Page 25 - ... that the single premium for an assurance of 1 on the life of x, with the return of the premium along with the sum assured, is equal to the annual premium to secure a perpetuity of 1 per annum, of which the first payment is made at the end of the year in which x shall die.