A new approach to the topic of life contingencies based on matrix analysis is introduced. Life insurance providing for cash-values is reinterpreted. It is proved that a consumer's optimal savings mix cannot include simultaneously life insurance and an endowment if there are transaction costs. The computation of the effective rate of return on life insurance is analyzed and seen to be related to the consumer's subjective survival probability. The purpose of the first of these companion papers is to introduce a new approach to the topic of life contingencies based on matrix analysis. Hopefully this approach will help the reader understand better the savings concept inherent in life insurance. For the sake of generality, the concept of a life contingent (LC) contract is introduced. An LC contract between an insurer and the policyowner, hereafter called consumer, is an arrangement the conditions of which depend upon the consumer's survival and under which the insurer is restricted to the role of a debtor.