At any time after sale and prior to the expiration of thirty years from the date of the contract, the purchaser or his successor in interest may pay all or any part of the purchase price due on any contract for purchase of state lands, but no payment shall be accepted, other than the first payment, for less than one-thirtieth of ninety-five per centum of the purchase price, nor be effective for credit on any date other than the anniversary of the date of the contract next following the date of tender.