Interface-based design is now considered to be one of the keys to tackling the increasing complexity of modern embedded systems. The central idea is that different components comprising such systems can be developed independently and a system designer can connect them together only if their interfaces match, without knowing the details of their internals. We use the concept of rate interfaces for compositional (correct-by-construction) design of embedded systems whose components communicate through data streams. Using the associated rate interface algebra, two components can be connected together if the output rate of one component is "compatible" with the input rate of the other component. We formalize this notion of compatibility and show that such an algebra is non-trivial because it has to accurately model the burstiness in the arrival rates of such data streams and the variability in their processing requirements. We discuss how rate interfaces simplify compositional design and at the same time help in functional and performance verification which would be difficult to address otherwise. Finally, we illustrate these advantages through a realistic case study involving a component-based design of a multiprocessor architecture running a picture-in-picture application.