Reports on the Madras Medical Fund / by Francis G.P. Neison.

Date:
1856
Catalogue details

Licence: Public Domain Mark

Credit: Reports on the Madras Medical Fund / by Francis G.P. Neison. Source: Wellcome Collection.

Provider: This material has been provided by the Royal College of Physicians of Edinburgh. The original may be consulted at the Royal College of Physicians of Edinburgh.

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    IY It has, however, been pointed out, that as the annuity is in fact payable half-yearly, the reversion to the whole annuity of £\ or one rupee would not be receivable, but only one quarter A' of a year’s annuity, and the reversion to it will be therefore worth only -JL and this is the N 4 increment to be added to the expression —- on account of the annuity being payable up to the uy date of death. It has also been shewn that because the annuity is payable by half-yearly instalments, the same expression receives the increase of '25, and consequently N A' A' 1 + A' ^L+.25+-JL=a, + -a5 + ^L=S + _rI y y ' ‘ 4 ™y payable by half-yearly instalments, and up to the date of death Present value of an annuity of ;£l or one rupee If therefore the values of annuities payable yearly in arrear be increased by the £\ -| - = —? the result will give the values of annuities payable half-yearly, and to the 4 4 date of death or marriage, as the case may be. In this manner were the values of the incumbent pensions in Tables XXIX., XXXIV., XXXVII., and Table 3 obtained. II.—Calculation of the Present Value of Annuities on the Joint Lives of Members and their Wives. Let lx — Number living at age x in the second column of Table XI. (members) and ly = Number living at age y in the second column of Table XII. (members’ wives) Vx = Lx-\-1 Probability of living one year at age x, and therefore \.px = \.lx+x — X./^. In like manner will \.px y = Log. of the probability of the joint survivorship for one year of the two lives age x and y; also let r = 0-80, Eight per cent, being the rate of interest adopted in the calculation of all the Tables in Report. 1 +r — P08, X. (]+r) = 0,03342j|fe, and therefore X. (1 + r) = 0'01671] 9. v 1 1+r 1 L08 •92592593 being the present value of £1 due one year hence, consequently