The monthly payment on a $$90,000,30-$year $(360-$month$)$ home loan is given by

$m(r)=\frac{90,000(\frac{r}{12})}{1-(1+\frac{r}{12}{)}^{-360}}$

where $r$ is the annual interest rate. Use Newton's method to determine the interest rate $r$ that allows you to make monthly payments of $$700$ per month.

The monthly payments will be $$700$ when $r=$

$($Simplify your answer. Round to six decimal places as needed.$)$