Is the price of gold against the dinar to be calculated at each installment due date, or only when the payment agreement is written for all installments?

It is permissible for the creditor and debtor to agree on paying for gold in installments, with each installment paid in dinars according to its price at the time of payment.

However, an agreement to pay in dinars in installments is impermissible because it is a currency exchange (sarf) which requires immediate possession (taqabud) and does not allow for deferral. It is permissible to exchange one currency for another, and it becomes a valid exchange (sarf bi 'ayn wa dhimmah) if possession is taken in the contract session.