You have a $$450$k mortgage on a house worth $$650$k$.$ You want to access $$50$k of that housing wealth $($home equity$)$ to pay for your child$$s college tuition. Your current rate is $5\%,$ but you know that rates have gone up$.$ If you get a $2$nd lien to finance this the cost is $13\%.$ What is the highest rate you would be willing to pay on a cash$-$out refi instead that would make it at least as good as a $2$nd lien? $($Hint: This is the opposite of the problem we did in$-$class.$)$

Group of answer choices

$7\mathrm{.}2\%$

$5\mathrm{.}8\%$

$6\mathrm{.}7\%$

$6\mathrm{.}3\%$