The present value of an annuity of £1 to endure for ever, reckoning the rate of interest to be 4 per cent., and assuming the first payment of the annuity to be made at the end of one year from the present time, is manifestly the sum of .£25. (Since £100 yields £ 4 in perpetuity, £25 will yield £1.) And if we suppose the termly payments about to fall due to belong to a person of a given age, so long as he may live, of which the present value has been ascertained to be £10, the difference, or the

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... sum of £15, will be the present value of tlie perpetual annuity to commence after the failwe of the given life. Noiv the value, at 4 per cent, of a perpetual annuity