2. Your neighbor is buying a new Tesla electric car. He has the following options to finance the purchase:

I. Pays $90,000 today (in time 0)

II. Buy under a "no payments for three years" program by agreeing to pay $110,000 three years from today (in time 3).

III. Make 60 monthly payments over 5 years of $1,750 payable at the end of each month.

(a) If the interest rate is 6% annually, calculate the present value of each option.

(b) At what interest rate do Option II and Option III have the same present value?

3. A family friend is retiring from work in the U.S. She is exactly 62 years old right now (time 0) and has the choice of taking her Social Security (a public pension program) right now or delaying according to the following schedule:

I. Early retirement (Age 62 exactly) $800 per month for life

II. Regular retirement (Age 66 years, 2 months) $1,000 per month for life

III. Delayed retirement (Age 70 exactly) $1,240 per month for life

If her expected life expectancy is 80 years old (exactly), what are the present values of the choices? (Assume r = 6% (annual))