This contract is valid and can be verbal. See the statute below which I linked earlier which limits when a contract must be in writing.
§ 9-1-4 - Statute of frauds
No action shall be brought:
(1) Whereby to charge any person upon any contract for the sale of lands, tenements, or hereditaments, or the making of any lease thereof for a longer time than one year;
(2) Whereby to charge any person upon any agreement made upon consideration of marriage;
(3) Whereby to charge any trustee under any express trust, or any executor or administrator, upon his or her special promise to answer any debt or damage out of his or her own estate;
(4) Whereby to charge any person upon his or her special promise to answer for the debt, default, or miscarriage of another person;
(5) Whereby to charge any person upon any agreement which is not to be performed within the space of one year from the making thereof;
(6) Whereby to charge any person upon any agreement or promise to pay any commission for or upon the sale of any interest in real estate,
unless the promise or agreement upon which the action shall be brought, or some note or memorandum thereof, shall be in writing, and signed by the party to be charged therewith, or by some other person by him or her thereunto lawfully authorized.