Michael is planning his retirement $30$ years from now.

Michael plans to withdraw $$15,000$ per month from his retirement account for $15$ years and then $$7,500$ a month for the following $10$ years. He will withdraw from this account for a total of $25$ years. He plans to have $$500,000$ for his heirs at the end of the retirement period. Michael will earn $4$ percent compounded monthly during the retirement phase of his life.

He plans to save $$500$ each month for the next $30$ years $($ordinary annuity$).$ What APR must Michael earn during his savings period assuming monthly compounding?

What APR must Michael earn during his savings period assuming monthly compounding? The format needs to be trhoguh excel $.$