I think you are missing the point of accrued liabilities. The whole point is that some sort of economic event has happened where the company SHOULD report a liability (and expense). For example, work that has been done for you but the company hasn't received the bill yet or wages that you owe your employees but haven't recorded as of the end of the period. So only the accrued liability will only show up on the B/S WHEN YOU ACTUALLY RECORD IT. For example, at the end of the period, one has probably not recorded the utilities expense for that period immediately. So before one makes the adjusting entry for the accrued expense, there is no liability recorded under "Utilities Payable" or some other similarly named account. Then when they record utilities expense for the partial period, the accompanying journal entry will increase the liability account. So... in essence, once accrued liabilities are actually accrued, they WILL show up on the b/s as a liability (this of course is only if one hasn't already paid) and the expense account will show up on the I/S.

Same exact thing happens for accrued revenues. So in the case of interest revenue, the revenue will not show up on the I/S nor will the accompanying a/r or cash account until the accrued revenue is actually accrued.

I am not the best person at explaining things but I hope this helps.