Bella and Marie are twins and both of them are turning $30$ today. Bella is hardworking and got a job immediately after graduation. As a reward, the father began putting $$5,000$ per year into a trust fund for Bella on her $20$th birthday, and he just made the $11$ th payment into the trust today on Bella's birthday. The father will continue to put in $$5,000$ per year until a $46$ th and final payment is made on Bella's $65$ th birthday. Bella's trust fund is earning $6\%$ per year.

The father did not do the same for Marie because she refused to look for a job after graduation and was just sitting at home over the past $10$ years. However, Marie has changed and got her first job today. So$,$ the father decided to set up a trust fund for Marie and start making his first annual deposit of $$5,000$ toriay. He will continue to make the same annual deposit each year for Marie until Marie turns $65$ also, when the $36$ th and final payment will be made. The father wants both Bella and Marie to have the same retirement nest egg when they retire at $65,$ but since the father start making contribution to Marie's trust fund much later, he needs to look for a trust fund that offer a higher return. What must Marie's trust fund return be in order for both Bella and Marie to have the same retirement nest egg when they turn $65?$ You must show all calculation steps, providing a final answer only will not get you full marks.