Greg Miller wants to buy a new automobile. The dealer has the exact car Miller wants and has given him two payment options: pay (1) the full cash price of $19,326 today or (2) only $2,000 down today and then take four more annual payments of $5,000 beginning one year from today. Miller doesn’t have the cash needed to pay the car’s full price, but he does have enough for the down payment. He can also obtain an automobile loan from his bank at 5% interest per year.
1. Verify that the imputed interest rate on the dealer’s loan is 6%. That is, show that the present value of Miller’s payments equal $19,326 (rounded to the nearest dollar) when discounted at 6%.
2. Which payment option should Miller accept?