Credit risk assessment is crucial for financial institutions, including savings and credit cooperative societies, to evaluate borrower creditworthiness and mitigate default risks. Traditional predictive analytics methods, such as linear regression and decision trees have been widely used. However, they often fall short of capturing complex, non-linear relationships inherent in financial data, leading to suboptimal risk predictions. This study introduces an enhanced predictive analytics model that uses polynomial logistic regression, augmented with Recursive Feature Elimination (RFE) and ridge regression. The model captures the intricate dynamics between key risk factors such as interest rates, income stability, and collateral value to give better performance. The model was trained and validated on credit risk dataset from Kaggle which achieved an Area Under the Curve (AUC) of 0.95, indicating a strong capability to distinguish between defaulters and non-defaulters. Comparative analyses with alternative machine learning models that include XGBoost and Random Forest demonstrated that while these models offer high predictive accuracy, they often require extensive hyperparameter tuning and lack interpretability. In contrast, the proposed logistic regression model balanced predictive performance with interpretability and computational efficiency, making it a better for credit risk management in financial institutions.