The impact of financial development on economic growth has received much attention in recent literature. However, there are potential discontinuities mediating finance–growth nexus that existing empirical studies have not rigorously examined. This study investigates whether the impact of finance on economic growth is conditioned on the initial levels of countries’ income per capita, human capital and financial development for 29 sub–Saharan Africa countries over the period 1980–2014 using a sample splitting and threshold estimation technique. Our findings suggest that, while financial development is positively and significantly associated with economic growth, below a certain estimated threshold, finance is largely insensitive to growth while significantly influencing economic activity for countries above the thresholds. The main conclusion drawn is that higher level of finance is a necessary condition in long run growth and so are the overall level of income and human capital.