$10.$ Viktoria just graduated from college. She wants to start saving for retirement by saving a fixed amount each month, starting one month from today. Assume monthly compounding during the working $($saving$)$ years. Exactly $41$ years from today, she wants to retire and have saved enough to be able to spend $$95,000$ per year for $22$ years, with the first withdrawal coming one year after the start of retirement. Assume annual compounding during the retirement years. Assuming an interest rate of $4\mathrm{.}4\%,$ how much does she need to save each month during her working years to achieve her goal?