Actuarial Science An Elementary Manual

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The first payment would accordingly be made at the end of the eleventh year. In forming tables of the amounts and present values of annuities it is advisable, for the reasons given in the last chapter, to work by a continuous process. Table of Amounts. It is probable that a table of (1 +i) n will have been formed pre- viously, and if so, the table of Sn\ is constructed very simply from the relation, Starting with the initial value, s\\ = 1, we have sl\ = SB\ + (1 + i) 5, and so on. For verifica...tion of the results, the value of s^| is calculated, from time to time, by the usual formula s^| = J -- 4 -- If, however, the table of (1 + i) n be not available, a formula for continuous working may be obtained as follows : Starting, as formerly, with the initial value, we multiply it by (1 + i), and adding 1 to the product, obtain the second value. By repeating this process we form the table. Table of Present Values. The table of present values can be formed without difficulty if a table of v n has been previously constructed.

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