For a single day as long as $K(t)$$K(t+1)$ includes the intraday cashflowscash flows it is the same, however if you do not simulate your cash balance interest rate you forget that your cash get compounded over time, which is slightly incorrect.
This is why someone suggested you simulate your cashbalancecash balance. This is more correct as well if you are not always 100% invested or if you have access to leverage as you get interest or get charged for being in credit/debit.