Any incorporated city or town having within its corporate limits an ancient family cemetery or burial ground or owning a cemetery or burial ground may make and enter into a contract with any interested party or parties obligating and binding the city or town to forever protect, maintain, and properly care for such cemetery or burial ground or for graves of individuals in the cemeteries or burial grounds owned by such city or town, upon terms and conditions as may be agreed upon and for such compensation as it may see fit to accept.