Customer churn refers to the loss of clients in the banking sector as a result of account closures or discontinuation of banking services. Banks may experience significant effects from this, including lower revenue, higher costs to attract new clients and reputational damage. In order to predict and analyze customer churn, this study examines the issue of customer churn in Zimbabwean banks and investigates the effectiveness of classical machine learning algorithms and deep neural networks. The study trains and evaluates several models, including logistic regression, decision trees, random forests, XGBoost, and a basic deep learning algorithm, using a dataset of customer data that includes demographic and banking-related features. The findings demonstrate that all models were successful in predicting customer churn with high accuracy, with the deep learning model outperforming the classical models. The small sample size and constrained feature set of the dataset are two limitations of the study that may affect how broadly applicable the findings are. The study's conclusion discusses how these practical ramifications will affect Zimbabwean banks practically and offers potential directions for future research.