This paper reports on a social discounting experiment conducted with university students in South Africa. In line with other social discounting task experiments, participants identify target individuals at different degrees of intimacy in their social network and then make 10 choices involving sums of money for themselves or their targets. For an altruism premium to exist, senders' donations to recipients should be positive, statistically and economically significant, and independent of relationship closeness. We hypothesize that in addition to the altruism premium for kin documented in the literature, there may be other premia for family in general and for partners and friends. We find that, apart from the "kinship" premium, there is a sizeable "intimacy" premium, which together translates into a substantial "family" premium. The study also finds a "friendship premium", as is documented in various experiments. The closeness of relationships among family and kin, especially close kin, has a significant and large effect on altruism. The results also attest to the importance of the extended family in regards to the "kinship" premium on altruism. These various premiums on altruism emphasise the importance of the supportive role of various social systems. Nevertheless, altruism within families and among close kin might also be enhanced by building more cohesive and stronger families using developmental social welfare programmes.