In a world where graduate incomes are uncertain (observation of the UK graduate wages from 1993 to 2003) and the higher education is financed through governmental loan (UK Higher Education Reform 2004), we build a theoretical model to show which scheme between an income contingent loan and a mortgage loan is preferred for higher level of uncertainty. Assuming a single lifetime shock on graduate incomes, we compare the individual expected utilities under the two loan schemes, for both risk neutral and risk averse individuals. We extend the analysis for graduate people working in the public sector and private sector, to stress on the extreme difference on the level of uncertainty. To make the model more realistic, we allow for the effects of the uncertainty each year for all the individual working life, assuming that the graduate income grows following a geometric Brownian motion. In general, we find that an income contingent loan is preferred for low level of the starting wage and high uncertainty