(a) Any two or more of the persons involved in or affected by an accident may enter into a written agreement for the payment of an agreed amount with respect to all claims of any of such persons because of bodily injury to or death or property damage arising from such accident, which agreement may provide for payment in installments, and may file a signed copy thereof with the department.

(b) The department, to the extent provided by any such written agreement filed with it, shall not require the deposit of security and shall terminate any prior order of suspension or, if security has previously been deposited, the department shall immediately return such security to the depositor or his personal representative.