Abstract: There are various interest rates of different terms in the actual financial markets. In order to calculate the life insurance rates under the condition of multiple interest rates, a linear programming model which is called "Income-outcome problem(IOP)" was established on the basis of the definition of maximum accumulation function, and its optimal value describes the maximum level of insurance payment that can be achieved through the rational arrangement of investment term of premium funds. Using local optimization method, two properties of the optimal solution of IOP are proved, and these properties show that the premium income fund should gives priority to the investment which has longer term (that is, larger interest rates) on the condition of meeting the insurance expenditures. For some typical life insurance product model, we give the structure of the optimal solution and list the calculated results of premium rate of two specific examples. The results show that the main factor in the calculation of premium rates is the longest term interest rate, followed by an comprehensive level of the different interest rates. The model of this paper also provides the basis for creating generalized theory of interest under the condition of multiple interest rates.

Key words: multiple interest rates, maximum accumulation function, linear optimization, income-outcome problem, life insurance pricing