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The primary goal of this paper was to look into the existence of a debt Laffer curve in the Bangladesh economy. Then, using this goal, find a debt level that maximises economic growth. This study used the debt-to-GDP ratio variable as the X-axis variable in the debt Laffer curve analysis. Real GDP is used as an economic growth indicator variable. Another goal of this study was to use the quantile regression technique to examine the relationship between external debt and economic growth. Quantile regression helped us investigate associations outside the dependent variable's mean, which often remain unseen. Aside from the external debt, various other economic growth indicators were evaluated. We used yearly time series data from 1977 to 2020 from the World Bank's World Development Indicators. Based on our findings, the debt Laffer Curve does not exist, so a debt threshold level cannot be established for the Bangladesh economy. The examination of quantile regression estimates allowed us to investigate previously unknown relationships, such as the negative marginal effect of the debt overhang variable on real GDP increases, as the real GDP increases. This pattern was not seen when we applied OLS.