We present the accounting system used for backing store management in the Mungi single-address-space operating system. The model is designed such that all accounting can be done asynchronously to operations on storage objects, and hence without slowing down such operations. It is based on bank accounts from which rent is collected for the storage occupied by objects. Rent automatically increases as available storage runs low, forcing users to release unneeded storage. Bank accounts receive regular income. A taxation system is used to prevent excessive buildup of funds on underutilised accounts. The accounting system is mostly implemented at user level, with minimal support from the kernel. As a consequence, the accounting model can be changed without modifying the Mungi kernel.