What is the ruling of Islamic law on financial transactions where profits are received in installments via post-dated checks, with the principal being received at the end of the year?

The ruling on this transaction varies depending on the nature of the agreement. If your father lends money and benefits from an additional percentage in return for the deferment, then this is usury (riba). However, if he purchases a commodity and it comes under his guarantee, then sells it to another person for a known deferred payment with an increase in price, this is a permissible Murabaha sale according to Islamic law, provided that the Sharia (definition)-compliant conditions are met.