Direct financing accounting

following, accounting, financing, interest

I’m having some trouble understanding the accounting basics behind a direct finance lease.
Say you are the lessor and are leasing an item to the lesse. The item cost you $100 and the lesse will pay you a total of $200 over 2 years.
So your initial journal entries would be
Lease receivable $200 (debit)
Leased Asset $100 (credit)
Unearned interest $100 (credit)
At the end of Year 1, the following entries would be done:
Cash $100 (debit)
Lease Receivable $100 (credit)
Unearned interest $50 (debit)
Interest Revenue $50 (credit)
Similarly, at the end of year 2, the following would happen:
Cash $100 (debit)
Lease Receivable $100 (credit)
Unearned interest $50 (debit)
Interest Revenue $50 (credit)
So it all makes sense to me so far you have written down the lease receivable to zero, you have recorded interest revenue of $100 over the two years.
But I don’t understand what happens to the Leased Asset we recorded at the beginning of the process, which is the $100 it cost to buy the item.
Shouldn’t it be zero now? It seems like I’m missing some other journal entry which would result in the leased asset value reaching zero by the time the lease terminates.
Any help would be appreciated