In this paper we investigate the effect of systematic longevity risk, i.e., the risk arising from uncertain future survival probabilities, on the attractiveness of different types of annuities. We consider a life-cycle framework with expected utility where an individual faces both investment and longevity risk. In contrast to existing literature we allow not only for idiosyncratic, but also for systematic longevity risk. When comparing the expected lifetime utility, conditional on the type of annuity which is purchased, we find for a 65-year old male that (i) systematic longevity risk reduces the attractiveness of annuities, (ii) when an immediate annuity is purchased, the expected lifetime utility is decreasing in the postponement period, (iii) when in the future purchasing an immediate annuities, the effect of the evolution of the survival probabilities on the optimal fraction of annuitized wealth is large, and (iv) the optimal annuity to purchase at retirement is a deferred annuity which starts to pay after only a short deferral period. However, when the purchase of an annuity with the optimal deferral period is compared to the purchase of an immediate annuity at retirement date, the utility gain is negligibly small.