This paper studies the possibilities of making prediction of stock market prices using historical data and machine learning algorithms. We have experimented with stock market data of the Apple Inc. using random trees and multilayer perceptron algorithms to perform the predictions of closing prices. An accuracy analysis was also conducted to determine how useful can these types of supervised machine learning algorithms could be in the financial field. These types of studies could also be researched with data from the Ecuadorian stock market exchanges i.e. Bolsa de Valores de Quito (BVQ) and Bolsa de Valores de Guayaquil (BVG) to evaluate the effectiveness of the algorithms in less liquid markets and possibly help reduce inefficiency costs for market participants and stakeholders.