Undergraduate and graduate students across the country rushed to consolidate their federal student loans this spring and summer in order to lock in lower interest payments before higher rates took effect on July 1. But frustrated students and executives at some companies that process the applications are accusing big lenders of violating federal regulations and slowing the process while charging higher rates in the meantime. In their defense, lenders say lags in processing applications are the result of the huge number of students who have applied to consolidate their loans. One company received 40,000 applications in June alone. Consolidation of debt enables borrowers to combine several loans in order to pay a single interest rate and make one monthly payment.