Consider a demand$-$paging system with a paging disk that has an average access and transfer time of $20$ milliseconds. Addresses are translated through a page table in main memory, with an access time of $1$ microsecond per memory access. Thus, each memory reference through the page table takes two accesses. To improve this time, we have added an associative memory that reduces access time to one memory reference if the page$-$table entry is in the associative memory.

Assume that $80$ percent of the accesses are in the associative memory and that, of those remaining, $10$ percent $($or $2$ percent of the total$)$ cause page faults. What is the effective memory access time?