Under the Michigan Motor Vehicle Sales Act MCL 492.112
(b) An installment sale contract [for a motor vehicle] shall be completed as to all essential provisions prior to the signing of the contract by the buyer and contain such other information as the administrator may require.
(c) An exact copy of the installment sale contract shall be furnished by the seller to the buyer without charge at the time the buyer signs the contract
(f) An installment sale contract shall provide for weekly, semi-monthly, or monthly payments of the time balance in substantially equal periods and amounts.
MCL 492.113 specifies various provisions and information which must be included in an installment sale contract for a motor vehicle. None of these mentions periodic statements.
Under MCL 492.128
(a) At any time after execution of an installment sale contract and within 1 year after termination of such contract, the holder of such contract shall furnish the buyer, upon request, with a complete and detailed statement of account showing:
All amounts paid by the buyer on account of the obligation, dates of payment and the allocation of such payments to reduction of the time balance, refinance charges, default charges, court costs, attorney's fees, expenses of retaking, repairing, storing, or otherwise.
All amounts credited to the buyer as rebates for prepayment and unexpired premiums on insurance cancelled.
The amount of the installment payments, accrued charges and expenses incurred, if any, which are due and payable.
The number and amount of installment payments to become due and payable, if any, and the due dates thereof.
(b) The buyer shall be furnished with 1 such statement of account without charge during the term of the contract or within 1 year after termination, and the holder may require payment of a fee of 50 cents for any additional statements.
(c) The holder shall furnish the buyer, upon request and upon payment of a fee of 50 cents, with a duplicate copy of the installment sale contract to replace the buyer's copy of such contract which is required to be furnished to the buyer without charge at the time of execution of the contract.
So it seems that the lender must provide a free detailed statement only once during the term of the loan, and may charge for additional statements. thre seems to be no provision on how rapidly the lender must provide the required statement, so it is probably "within a reasonable time".
Under MCL 492.129
(a) Whenever payment is made on account of any installment sale contract, the person receiving such payment shall, at the time of receiving such payment, furnish to the buyer or to the person making the payment on behalf of the buyer, a complete written receipt therefor, if requested. A receipt must be given if payment is made in cash.
(b) Such receipt shall show the date of payment, the amount of the payment, and shall identify the obligation to which such payment is applicable.
(c) When issued for payments made at any office of the holder or mailed to such office, which payments are applied to reduction of the time balance, such receipt shall, if requested by the buyer, also set forth the unpaid time balance remaining due after crediting such payment. If such payment includes default charges authorized by this act, the amount of such default charges shall be set forth on the receipt independently of the payment applied to reduction of the time balance.
(d) When the buyer elects to make such payments by mail, the holder may require the buyer to supply a self-addressed stamped envelope as a condition for mailing such receipt to him, if he has been previously notified of such condition.
Such a receipt, while not a full statement, should serve most of the purposes of a statement, particularly in showing the remaining balance due, particularly in connection with the requirement that the lender provide at any time, for a nominal fee, a copy of the sales contract, which must include the schedule of payments. Note that under section 492.121, the purchaser is always allowed to prepay all or part of the balance due, and unearned interest on such prepaid balance must be refunded, or omitted from future payments.