Artificial Neural Networks as one of the Artificial Intelligence applications, which is the leading candidate for the greatest innovation of the century, has been started to be used in solving the complex problems of the economy for a while. Among them, predicting the exchange rate is one of the utmost important complex issues to be determined especially for the small open economies, such as Turkey, where the changes in exchange rate influence all the other variables in the economy, from macro variables to micro-ones. This paper aims to analyze the exchange rate determination between Turkish Lira and American Dollar by using Artificial Neural Networks through the Monetarist Model. As a result, very close results to the real values were obtained. It can be said that although in exchange rate estimation both Artificial Neural Networks -Levenberg Marquardt and Artificial Neural Networks-Quasi-Newton models give good results, the Artificial Neural Networks -Levenberg Marquardt model is more successful in general terms.