As a New Year's gift to yourself, you buy your roommate's $1976$ Ford Pinto. She has given you the option of two payment plans. Under Plan A$,$ you pay $$500$ now, plus $$500$ at the beginning of each of the next two years. Under Plan B$,$ you would pay nothing down, but $$800$ at the beginning of each of the next two years.

a$.$ Assuming the interest rate is $10\%,$ the present value of Plan A$\text{'}$s payment is $.$ That of Plan B$\text{'}$s payment is $.$ You should, therefore, choose $.$

b$.$ Assuming the interest rate is $20\%,$ the present value of Plan A$\text{'}$s payment is $.$ That of Plan B$\text{'}$s payment is $.$ You should, therefore, choose $.$

c$.$ When the interest rate rises, the present value of the plan featuring a down payment by proportionately than that of the plan that does not feature a down payment. This is because down payments aren't discounted.