Do you want to offer your client a lower equivalent rate by providing cash back at closing? In this case you will have a contract rate and a rate that can be advertised if a cash rebate is applied. The monthly payment will be calculated at the lower/discounted rate.
Providing the cash back indicated will give the client the equivalent of the lower rate. You must be able to increase the amortization slightly to bring the monthly payment down. You will need to lower the payment more than necessary due to the amortization ending up with a fraction of a month. The client would then need to increase the monthly payment. It is assumed that the cash back is applied back to the mortgage on the day it funds.
If you must use the contract payment that your client would have at the contract rate use this calculator.
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