Without using Excel functions or a financial calculator, please solve the question provided below. Be sure to include all steps by using the correct formulas in solving the question.
Tammy wishes to save money to provide for her retirement. Beginning one month from now, she will begin depositing a fixed amount into a retirement savings account that will earn 10% compounded monthly. She will make 420 such deposits. Then, one year after making her final deposit, she will withdraw $75,000 annually for 20 years. The fund will continue to earn 10% compounded monthly. How much should the monthly deposits be for her retirement plan?