In our study we analysed the effect of the introduction of an instant payment system in Hungary, using a large number of transaction level data of an extended time period, simulating the operation of the payment system. We analysed the two main theoretical models of instant payments: instant settlement in central bank money, and instant clearing with prefunded cyclical settlement. For both models we estimated the effect of using low and high transaction limits. We differentiated three liquidity costs associated with the operation of such a system. First we estimated the impact on settlement queues in the real-time gross settlement system and calculated the costs of extra liquidity needed to dissolve the queues and support the continuous operation of the system. In the second step we estimated the liquidity needs of a prefunded instant payment system by different confidence levels and prudential requirements. Lastly, we analysed the effects of the different models on the stability of the payment system. The results clearly show that the costs associated with the dissolution of queues are marginal because retail payments comprise a very small percentage of the inter-bank payment flows, thus the instant payment system would not generate additional settlement queues. On the other hand, liquidity needs of a prefunded model can be significant, especially with high collateral confidence levels and high transaction value limits. However, these liquidity needs can be lowered by seasonal adjustments to the prefunded amounts and by using a robust but rational collateral confidence level. We also show that these costs are relatively higher for institutions with fewer customers as their payments turnover is more volatile, and so they have to make relatively larger prefunded deposits.