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 lower rate that can be advertised/used for your client if a cash rebate is applied. The monthly payment will be calculated at the higher/contract rate.
Providing the cash back indicated will give the client the equivalent of the lower rate. It is assumed that the cash back is applied back to the mortgage on the day it funds.
If you want to use the monthly payment that your client would have at the lower rate use this calculator.