these is my question

39. Home Mortgage You plan to take out a 30-year fixed-rate mortgage and you want your monthly payment to be $1200. The amount of the loan you can afford depends on the interest rate you will have to pay. Let A(r) be the amount of the money you can borrow if the interest rate is r% per year, compounded monthly. Interpret the given equations, including units. (a) A(5) = 223,537.94 (b) Would you expect the sign of A'(r) to be positive, negative, or zero? Why? (c) What are the units for A'(r)? (d) A'(5) = -25,449.21 40. Credit Card Payments A credit card statement includes information on how long it will take to pay off the card if you make only the minimum payments and how long it will take if you make larger payments. Let M(p) represent the number of months it will take to pay off your credit card if you make a monthly payment of $p (assuming no additional charges are made). (a) Explain what M(25) = 50 means. (b) Would you expect M'(p) to be positive, negative, or zero? Why? (c) What are the units for M'(p)? (d) Explain what M'(25) = -3 means