We compare two alternative approaches for coupling macroeconomic growth models (MGM) and energy system models (ESM). The hard-link approach integrates the techno-economics of the ESM completely into the MGM and solves one highly complex optimisation problem. The soft-link leaves the two models separate and energy supply functions are integrated into the MGM that are derived from the optimal solution of the ESM. The energy supply functions relate the price of energy computed with the ESM to the quantity of energy computed with the MGM. An iterative process exchanges price-quantity information between the models. Hence, the soft-link leads to an energy market equilibrium. But energy supply functions do not consider variable interest rates that influence the energy supply functions. This is due to the fact that ESMs are partial models that assume an exogenous interest rate; however the interest rate is computed endogenously in MGMs. This missing interaction leads to a capital market dis-equilibrium in the soft-link compared to the hard-link approach inducing a mis-allocation of investments. Extending the soft-link approach by also considering the time variable interest rate of the MGM does not improve the results. Though the computational complexity is greater the hard-link approach assures simultaneous energy and capital market equilibrium.