The account was valued at $6000000 at time0, $6380000 at time1, why when contribution was added at the begining, it has to be added to $6000000 (so it does not contain the contribution, so need to be taken account), but why when the contribution was added at the end, it has to be removed from $6380000 (why it already contain the contribution, seems not consistent)??

to calculate the rate of return … if the contribution was received at the beginning of the month - the cnontribution also earned returns during the month.

so return = [6380 - (6000+80)]/(6000+80)

If the return was received at the end of the month - it did not earn any returns at all.

You calculate the rate of return by comparing the ending value after investment return to the beginning value available for investment.

Thus, if you add money at the beginning of the period, it’s available for investment, so you include that money in the original amount to compute the return. If you add money at the end of the period, it is not the result of investment return, so you don’t include it in the ending amount to compute the return.

Thanks for the answer. The problem is why the value of inital amount 6000000 does not include the 80000 if it is added at the begining (why not the initial amount is 5920000 and adding the 80000, it is 6000000. But clearly the ending amount 6380000 include the contribution when that is added at the end. I am confused there.

so it is not included in the rollover amount from previous period, but is included in the ending balance of this period. (which will rollover to the next period).