7. Lease vs. Buy. Analyze the financial differences between renting and purchasing a car. To simplify the analysis suppose you have decided on a particular vehicle, so the price and value of the car are fixed Suppose that the value of a car declines in a manner similar to compound interest so that: V(t) = P(1-r) with P the purchase price, r the annual depreciation rate, t the number of years Suppose that you have the option to lease the car for 2 years or to take out a loan for the car which has a term of 5 years (a) Assume the interest rate for the loan is 5% Construct a loan amortization table for the loan and determine the monthly payment assuming interest is com pounded monthly and zero down payment (b) Determine the amount of interest paid on the loan after two years. Call this I. This is the price of credit for this loan for the first two years (c) Determine the value of the car after two years assuming a 5% depreciation rate In order to compare the price of owning to the price of the lease, suppose you sell the car after 2 years at its current value. Subtract that value from the out- standing balance on the loan. Take the remainder and add it to I to find the cost of buying this car for 2 years (d) To estimate the lease price, consider the car seller's position. Since the ambient lending rate for the buyer is 5% we might use this as a baseline for the seller. If the seller leases the car, they receive monthly payments from the leasee, and at the end of the lease they receive the used car. Assume the seller has the full principal invested at 5% compounded monthly for 2 years. Subtract the value of the car after 2 years from the accumulated value of the cars price. Determine a level monthly annuity for the lease which adds up to this difference, this would be the minimum the seller could charge to match the time value of the lease under the same conditions as the buyer. (e) Compare the payments made by the buyer in the buy and lease situations, deter- mine which choice is better. (Note we are oversimplifying the cost of ownership, and are ignoring things like variations in mileage and damage which can further complicate the comparison)