Noelle is a $0$ year old baby and she will go to college at age $18($i$.$e$.,$ in $18$ years$).$ Annual tuition at her dream college will be $$50,000$ at that time. Assume that Noelle will spend $4$ years in college and that the college savings account can earn $7\%$ per year. You will pay the tuition at the beginning of each college year $($i$.$e$.,$ first tuition is due in $18$ years, second tuition due in $19$ years, and so on$).$

Noelle$$s mom is planning to save the fixed amount at the end of each year for the next $18$ years starting one year from today to pay for his education.

What is the fixed annual amount that Noelle$$s mom has to put away each year for the next $18$ years?