A loan of $75000 is repaid over 20 years by monthly payments of $562.5. Use two iterations of the Newton-Raphson method starting with the initial guess of an annual interest rate of 12% (compounded monthly), to determine the annual interest rate.
NOTE: If P is borrowed at a rate of r per period, and is repaid over N periods by payments of Y, then: $Pr+Y[(1+r)^{-N}-1] = 0$.

If $f(r)=75000 r+562.5 [(1+r)^{-400}-1]$
$f'(r)=$

Annual interest rate $=$
Report your answer to 3 decimal places.

(you will lose 25% of your points if you do)