Home equity: When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. If your mortgage is for P dollars, and if the term of the mortgage is t...

Home equity: When you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E, in dollars, after k monthly payments is given by

Here r is the monthly interest rate as a decimal, with r = APR/12. Suppose you have a mortgage of $425,000 at an APR of 9% and a term of 30 years. How long does it take for your equity to reach half of the amount of the original mortgage? (Round r to four decimal places.)