Consider a mortgage for $750,000 with a constant interest rate of 5% (r = 0.05) and a monthly payment p = $4000. 1. Implement Euler's method for Eq. (3) with step size h = 0.5. Run the method until the mortgage is paid off and determine when it is paid off. Note: in reality, the mortgage is paid off when its value is zero. However, due to errors in the computations (both discretization and roundoff), it is likely that Euler's method will not produce an exact value of 0 for the mortgage value for any time. To account for this, consider the mortgage to be paid off when its value first becomes negative. 2. Plot the numerical solution A(t) and the true solution to Eq. (3) with the parameters given here on the same graph and compare the two. 3. Repeat the previous item for a step size h = 0.01 and comment on the difference. If the borrower makes a monthly payment of p dollars, the model becomes, assuming that the payments are distributed continuously throughout the year, A' = rA 12p, A(0) = Ao (3) Consider a mortgage for $750,000 with a constant interest rate of 5% (r = 0.05) and a monthly payment p = $4000. 1. Implement Euler's method for Eq. (3) with step size h = 0.5. Run the method until the mortgage is paid off and determine when it is paid off. Note: in reality, the mortgage is paid off when its value is zero. However, due to errors in the computations (both discretization and roundoff), it is likely that Euler's method will not produce an exact value of 0 for the mortgage value for any time. To account for this, consider the mortgage to be paid off when its value first becomes negative. 2. Plot the numerical solution A(t) and the true solution to Eq. (3) with the parameters given here on the same graph and compare the two. 3. Repeat the previous item for a step size h = 0.01 and comment on the difference. If the borrower makes a monthly payment of p dollars, the model becomes, assuming that the payments are distributed continuously throughout the year, A' = rA 12p, A(0) = Ao (3)