Many practical systems involve sensors that provide signals at slow sample rates. Guaranteeing the intersample performance is a fundamental problem in controlling such systems. Two multirate model predictive control schemes are presented as solutions to this problem. In the first control scheme, intersample responses are estimated and used as compensation for the missing measurements of the controlled output. This scheme can therefore operate at the desired fast rate. The second scheme updates the control action at the slow rate that the output is sampled, but it is different from conventional techniques. This scheme finds intersample responses using a modified Z transform, and produces the control variable by optimising a performance index that accounts for both sample and intersample behaviour. Numerical simulations demonstrate that the two multirate algorithms exhibit improved time responses compared to the conventional approach.