Is zakat obligatory on a loan taken to purchase an apartment, when a year has passed before the apartment's value was paid?

If the debt consumes the Zakat-eligible money or reduces it below the nisab (minimum threshold), then there is no Zakat due, unless you have other non-Zakat-eligible money that exceeds your basic needs. In that case, you should offset the debt with that money. If it covers the debt and a nisab remains, then Zakat is obligatory; otherwise, it is not. If the loan was based on a usurious contract, then the money must be returned to the bank, and no Zakat is due from you on it, because it is not your property.