Beatrice is 55 years old and will retire in 10 years, when she turns 65. She has saved $1,000,000, which she keeps in an investment account that earns 8.0% annually. She expects to additionally contribute $30,000 annually into this account until she retires and will make the investments at year-end. Suppose that, upon retirement, she will reallocate her portfolio to make it more conservative, such that she expects to earn lower rate of return. Because all of her parents and grandparents lived approximately until the age of 90, she expects to live until she turns 90. She expects to need to withdraw $150,000 each year during her retirement, making such withdrawals as the beginning of each year.

Based on these facts, what rate of return will Beatrice require on her retirement savings, during her retirement years?