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Economic growth and convergence issues arise in humanity continually, especially in developing countries. With Rwandan and Peruvian common vital economic variables from 1960 to 2017, we analyze their economic growth, causality, and convergence. The cointegration shows the long-run equilibrium correlation among the explained and explanatory variables, indicating the causality occurrence. The causality direction is defined by the Error Correction Model (ECM) using the Chi-square (χ2) short-run test, long-run T-test, and joint F-test statistics. The estimated values support a generalized Broadwell model equation with linear and quadratic terms. Through ANOVA with the F test, the economic convergence scenario for the two countries is testified. Thus, joint countries' strategies for economic improvement are suggested with the reduction of unnecessary losses.