Interest in conventional economic models is a key and regulator factor. However, there are many debates on the rejection or confirmation of monetary interest rates based on their origins. Some of these origins are objective, such as the productivity of capital and the population, and some like the time preference, the liquidity preference, and the convergence of the utility function, are subjective. This study, in considering the critical views of monetary interest rate, offers a model that, while eliminating interest rate, seeks to exploit the benefits of interest economies, such as consumption, savings, and accumulation of capital. The intergenerational exchange is shaped in the framework of the overlapping generation model and the population is a positive factor that grows as production grows. In this model, money is issued only once by the government and it is concluded that the continuation of the economy will increase the real value of fixed currency units. The liquidity preference will be eliminated in this model, and as a result, there will not be Hoarding money, and the allocations will be optimal, and this optimality will be permanent.