An inverse floater is a type of security whose payments move opposite to short$-$term interest rates. The security is ordinarily structured so that no matter how high interest rates rise, the payment cannot be negative. And no matter how low interest rates drop, the payment cannot exceed some specified cap, e$.$g$.,7\%.$ Consider the following specific case: if the prevailing short$-$term rate is X$,$ the inverse floater pays

Y $=100\backslash$times max$(0\mathrm{.}07$ X$,0)$

on $$100$ of face value. $($The notation "max$(0\mathrm{.}07$ X$,0)"$ means use whichever is larger, $0\mathrm{.}07$ X or $0.)$ Suppose the distribution of the short$-$term rate X at the next payment date is given by the following table:

$0\mathrm{.}040\mathrm{.}060\mathrm{.}070\mathrm{.}080\mathrm{.}09$

$0\mathrm{.}30\mathrm{.}20\mathrm{.}20\mathrm{.}150\mathrm{.}15$

Find the expected payment

$.($Hint: You need to figure out the value of the payment Y for each value of X$).$

Write your answer in percent, omit the $\text{'}\%\text{'}$ sign.