# mortage with monthly payment - mathematical modeling

$Question:$ Suppose that $x_n$ is the amount owed on a mortgage after n years, $\$m$is the monthly repayment and$r$is the annual percentage interest rate charged on the amount of the mortgage outstanding. (i) Derive a difference equation satisfied by$x_n$. (ii) Solve the difference equation derived in (i) for a loan of$\$M$ to be repaid over $N$ years and hence determine what the monthly payment should be.

(iii) If the interest rate is $5\%$, show that the monthly repayment on a loan of $\$50,000$to be repaid over$25$years is$\$295.64$.

(iv) What is the total amount paid back on the loan?

$My$ $answer$ $so$ $far:$