Dual tasks of capital accumulation processes and loan repayment

Abstract

Purpose: the paper deals with the processes of continuous repayment of the loan and continuous accumulation of capital at a continuous simple interest. The problem of maximizing the accumulated amount on straight trajectories with the limitation of the total amount of deposits is solved. A similar problem − minimizing the amount of payments when repaying the loan, was solved in the article [9] on a wider class of trajectories. There are connections between the processes of loan repayment and capital accumulation. Discussion: the peculiarity of the work is that the processes of accumulation and repayment are considered as continuous, which makes it easier to study them using simple and complex continuous rates. In addition, as in previous works, it is assumed that money has both temporary and timeless value. Results: it is shown that both problems can be represented as linear programming problems and can also be solved by the simplex method. For both problems are constructed dual in relation to them. It turns out the economic meaning of their decisions. As the examples show, the results of the work can be easily translated into practical terms.