Suppose you take a $3/1$ interest$-$only, $30-$year ARM for $$220,000\mathrm{.}00$ with an interest$-$only contract rate of $5\%$ and a following rate of $8\mathrm{.}25\%$ in year $4.$

 Assume you pay $2$ discount points.

Suppose that the contract rate in year $5$ is $8\mathrm{.}5\%$ and this contract rate stays constant from years $5$ through $30.$  What is the APR?