Cynthia would like to begin planning for retirement. Her grand parents agree to put in some amount as her 40th birthday gift that she plans to deposit in a bank account earning 3.5% per year compounded yearly. Cynthia is willing to begin saving $3,000 on her 41st birthday, and increase that amount by 4.5% every year. She would like to make the last deposit on her 49th birthday and then get $50,000 on her 50th birthday. After this should she would like to keep getting an amount greater than that by 6% every year till her 55th birthday. Also, she would like to have $125,000 in her account after removing the living money for the coming year on her 55th birthday to live after that. How much money should her grandparents gift her on her 40th birthday?