The ordinary formula for the value of a reversionary annuity, ax–axy, is not strictly applicable to the cases which occur in practice. For it assumes that the first payment of the annuity is made at the end of the year in which y dies, and the last payment at the end of the year before that in which x dies. But the conditions which prevail in practice are different; for whenever a reversionary annuity is granted, it will run from the death of y, and the first payment will be made twelve months after that death, i.e., on the average, six months later than is assumed in the above formula. On the other hand, the reversionary annuity will in practice be payable up to the day of the death of x; or, on the average, a full year's payment will be made six months later than the last payment is made according to the above formula.