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METHOD OF CALCULATION.

LET the age be reckoned 35.—The value (interest being at 4 per cent.) of 100l. payable at the death of a person aged 35, provided he survives another person of the same age, is £14.55, by Mr. Simpson's Problem quoted in Question XII. Vol. I. p. 42, and by the correction explained in Vol. I. p. 35 and 69: deducing the values of the longest of the two lives from Tables VI. and VII. in this volume, by the rule in the Note p. 43, Vol. I.

This gives the value sought for this Table, on the supposition that it is certain, that a married man will at his death leave children under age. If one tenth of those who die widowers leave either no children, or none under age, then this value must be diminished, on that account, one tenth. And if, besides, one in five of all who are left widowers marry a second time wives not older than themselves, one half at least of whom, (that is, one tenth of all that are left widowers) must be reckoned to die in a 2d or 3d marriage; then the same value must be diminished again another tenth; that is, a fifth in all; and this will make it £11.64, (or 117. 13s. nearly) which is the value in a single payment given in the Table.- -Divide £11.64 by 14.98 (the value increased by unity of a life aged 25

by

by Table VI. in this Volume) and the quotient will be .777 (or 15s. 6d.) which is the value in annual payments during the single life, the first payment to be made immediately.

In this Table no allowance has been made for the inequality of age between a man and his wife, and for the chances of survivorship being, on this and other accounts, much against him in marriage. The values in it, therefore, are probably much too high.

Had the value just determined been deduced from the Sweden Tables for males and females taken collectively, it would have been in the single payment 10l. 16s.; in the annual payment 138. 7d.Had the wife been reckoned 29 (the husband being 35), it would have been in the single payment gl. 48. 6d.; in the annual payment 118, 7d.

A society, therefore, for relieving orphans on this plan, might safely adopt lower payments than those in this Table; nor would there be any danger from the admission of bad lives,

TABLE

TABLE LVIII.

Shewing the present Value of an Annuity of 10%. for five years; 201. for the next succeeding five Years; and 30l. for the whole of Life after Ten Years; payable quarterly; and to commence at FIFTY-FIVE Years of Age.-See the Reference to this and the following Table in Vol. I. p. 148.

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TABLE LIX.

Shewing the Values of an Annuity of 101. for five Years; 201. for the next succeeding five Years; and 301. for the whole of Life after Ten Years; payable quarterly; and to commence at SIXTY Years of Age.- -See Vol. I. P. 148..

Age of the
Purchaser.

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These last two Tables have been calculated by the rules in Vol. I. p. 18, 19, &c.

The probabilities of the duration of life have been supposed nearly the same with those in the Northampton Table of mortality.

The interest of money has been reckoned at 3 per cent.; and it must be further remembered, that the values in each of the 24 and 3d columns are the whole values.

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APPENDIX.

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