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

I. Pays $35,000 today (in time 0) and $40,000 in one year (time 1)

II. Make payments under an increasing schedule as follows:

Time 0 $10,000

Time 1 $12,000

Time 2 $14,000

Time 3 $16,000

Time 4 $18,000

Time 5 $20,000

III. Make 78 monthly payments over 6.5 years of $1,200 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?