EXAMPLE 4-10 How Much Is a Lifetime Oil Change Offer Worth? "Make your best deal with us on a new automobile and we'll change your oil for free for as long as you own the car!" If you purchase a car from this dealership, you expect to have four free oil changes per year during the five years you keep the car. Each oil change would normally cost you $30. If you save your money in a mutual fund earning 2% per quarter, how much are the oil changes worth to you at the time you buy the car? Solution In this example, we need to find the present equivalent of the cost of future oil changes. The cash-flow diagram is shown below. Notice that P occurs one time period (a quarter of a year, in this example) before the first oil change cash flow (A). 250 254 58 Time of Purchase A=$30 2 3 19 20 End of Quarter P-? The interest rate is 2% per quarter, and a total of (4 oil changes/year x 5 years) = 20 oil changes (cash flows) are anticipated. P=$30(P/A,2%, 20) = $30(16.3514) = $490.54