You are $24$ years old now, and just graduated from college. You got your first job after graduation, and they will pay you $$57,331$ per year. Inflation is expected to increase at $4\%$ per year for the foreseeable future. If you plan to work from age $24$ to $62,$ then retire, and you expect to live until age $100,$ how much should you save each year for retirement while you are working? Assume you$$ll earn $10\%$ in your working years and $5\%$ in retirement. $($Do all calculations on an annual basis, do not round intermediate calculations, you can round your final answer to two decimal places.$)$

Hint: Start by finding the income you'll need in retirement. Then find the amount needed in savings to support that income level. Finally, find the amount needed to save each year while working in order to reach that savings need.