$17.$ Unearned Revenue A rental company owns a building from which it leases out multiple offices. During the year, it received the following advance rental payments for one$-$year leases from separate tenants: $$24,000$ in June, $$36,000$ in August, and $$12,000$ in October. The leases started the first of the month following the payment. Assume that these are the only advance rental payments received and that no adjusting entries were made during the year. a$.$ Find the balance of the unearned rent revenue account at year$-$end on December $31.$

Also, find the amount of the adjustment needed at year$-$end

b$.$ Journalize the adjusting entry to record the revenue earned.