E$.$ Jay and Patty's son Jimbo just turned $8$ years old today and they decided to plan for his education and housing costs. Jimbo is expected to start college $10$ years from today on his ${18}^{th}$ Jay and Patty want to plan for $4$ years of college and estimate it will take $$40,000$ each year $($at the start of each year$)$ for each of the $4$ years to pay for the education. In addition, Jay and Patty plan to buy Jimbo a condo $($near campus$)$ at an estimated cost. of $$150,000$ on his ${20}^{th}$ birthday $($after he moves off campus beginning his Junior year$).$ Jay and Patty plan to deposit $$50,000$ today $($on limbo$\text{'}$s $8^{th}$ birthday$)$ in a stock fund that they expect to earn a return of $8\mathrm{.}5$ percent up until Jimbo's ${18}^{th}$ Birthday, at which time they plan to sell the stock fund and put all of the proceeds into a college savings account for Jimbo's education and housing costs, In addition, on each of Jimbo's $9^{mh\text{t}\text{h}\text{r}\text{o}\text{u}\text{g}\text{h}}{18}^{th}$ birthdays, Jay and Patty expect to annually deposit $$12,500$ into this same college savings account. Assuming the college savings account wili earn a $5\mathrm{.}0\%$ interest rate while Jimbo is in college, what interest rate must the college savings account earn during the next $10$ years in order to make the withdrawals necessary from the college savings account to pay for college and housing costs?

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