As a parent, you want to save for your child's college fund. You see that currently, one year of tuition is approximately $$35,000.$

You decide to deposit $$125$ in an account for your child$$s college fund each month from when they were born. You want the total deposit to grow to cover or equal four years of the current tuition of $$35,000$ over the $18$ years.

At what nominal rate did the the investment grow?

Suppose with inflation, costs in tuition rose approximately by $9\mathrm{.}8\%$ each year since you started investing into the fund. Based on the cost of one year of tuition being $$35,000$ now, how much must you invest each month at the annual rate found in the previous part to have enough for four years of tuition in $18$ years?