Case 1. Car

John can afford to spend $500 per month on a car. He figures he needs half of it for gas, parking, and insurance. He has been to the bank, and they will loan him 100% of the car's purchase price.

a) If his loan is at a nominal 12% annual rate over 36 months, what is the most expensive car he can purchase?

b) The car he likes costs $14,000 and the dealer will finance it over 60 months at 12%. Can he afford it? If not, for how many months will he need to save his $500 per month?

c) What is the highest interest rate he can pay over 60 months and stay within his budget if he buys the $14,000 car now?

Case 2. Mortgage

a) Assume mortgage payments of $1000 per month for 30 years and an interest rate of 0.5% per month. What initial principal or PW will this repay?

b) Assume annual mortgage payments of $12,000 for 30 years and an interest rate of 6% per year. What initial principal or PW will this repay?

c) Assume annual mortgage payments of $12,000 for 30 years and an interest rate of 6.168% per year. What initial principal or PW will this repay?

Graphs: For each case (car/mortgage) at least one graph, which you can use to back up your discussion. For example, plot the interest payment + principal payment + balance.