A person committing a tort may, before or after an action is brought, tender to the person injured such an amount of damages as in his judgment will cover the injury; and, if the same shall be rejected, he may deposit the amount in the office of the clerk of the superior court of the county of his residence as a continuing tender; and, if the jury trying the cause shall give no more damages than the amount tendered, the plaintiff shall recover no costs accruing subsequently to the time of the tender.