You are thinking about buying a new car. After all haggling with the dealer and after including all additional chargers like the Acquisition Fee, license plates, and sales taxes, your “out-the-door” price is $35,222.74. You decide to lease your new car. The MSRP (Manufacturer’s Suggested Retail Price) plus Options is (MSRP+Options) = $38,740.00. The car has an estimated Residual Value (should be close to the price at which you can buy the car at the end of the lease but might not be exact) of 58% of $38,740.00; that is, Residual Value = $22,469.20. This leaves an amount to be depreciated of Depreciation = $35,222.74 – $22,469.20 = $12,753.54. (Notice that the (MSRP+Options) was only used to get the Residual Value of the car.) You are told that your monthly payment is $504.26 on a three-year lease. [You don’t need all of the information in the present paragraph to answer the questions I am about to ask, but I include this information in case you are interested. The monthly payment of $504.26 consists of two parts. The first part is called Monthly Depreciation. This is simply $12,753.54/36 = $354.26. The other part is called Monthly Rent Charge. In this case, it is (.08011/12)($22,469.20) = $150.00. The sum of $354.26 and $150.00 is the monthly payment of $504.26.]

There are several numbers floating around in the previous paragraphs; but, here is the bottom line: You agree to a three year lease on a car that has an out-the-door price of $35,222.74. The car has a residual value of $22,469.20 after three years. You agree to pay $504.26 per month on the lease. Question: What is the implicit interest rate in this transaction?

One more question: Although the “out-the-door” price already includes the sales tax of 9.25% in Cook County, the City of Chicago charges an additional 8% tax on every monthly payment, or $40.35 = (.08)($504.26) in this case. The total monthly payment therefore becomes $544.61 = $504.26 + $40.35. Question: What is the implicit interest rate in this transaction?