THIS IS DONE ON MAPLE PLEASE

restart; We prepare the following formulas: the future value of a lumpsum A (if interest is compounded n times per year) is L := (A, r, n, t) -> A*(1 + r/n)^(n*t); NULL; the future value of a lumpsum A (if interest is compounded continuously) is Lc := (A, r, t) -> A*exp(r*t);

the future value of a stream of equal payments P is (with payments at the end of each period) S := (P, r, n, t) -> P*((1 + r/n)^(n*t) - 1)*n/r;

the Balance on a mortgage (or similar loan or annuity) is B := (A, r, n, t, P) -> A*(1 + r/n)^(n*t) - P*((1 + r/n)^(n*t) - 1)*n/r;

Problem 5: Suppose we can afford $1000 a month toward a mortgage. a. If the interest rate is r=0%, how big of a mortgage can we afford? (use common sense, the formula will not work for r=0) b. If the interest rate is r=5%, how big of a mortgage can we afford? solve(B(A, 0.05, 12, 30, 1000) = 0, A); c. If the interest rate is r=10%, how big of a mortgage can we afford? solve(B(A, 0.10, 12, 30, 1000) = 0, A); d. Draw a graph for the amount of mortgage we can afford as a function of the interest rate r, with r ranging from 0% to 20%.