Automobiles are often leased, and several terms are unique to auto leases. Suppo

Question

Automobiles are often leased, and several terms are unique to auto leases. Suppose you are considering leasing a car. The price you and the dealer agree on for the car is $29,300. This is the base capitalized cost. Other costs added to the capitalized cost price include the acquisition (bank) fee, insurance, or extended warranty. Assume these costs are $900. Capitalization cost reductions include any down payment, credit for trade-in, or dealer rebate. Assume you make a down payment of $3,500, and there is no trade-in or rebate. If you drive 12,000 miles per year, the lease-end residual value for this car will be $20,500 after three years. The lease or "money" factor, which is the interest rate on the loan, is the APR of the loan divided by 2,400. The lease factor the dealer quotes you is 0.00271. The monthly lease payment consists of three parts: a depreciation fee, a finance fee, and sales tax. The depreciation fee is the net capitalization cost minus the residual value, divided by the term of the lease. The net capitalization cost is the cost of the car minus any cost reductions plus any additional costs. The finance fee is the net capitalization cost plus the residual, times the money factor, and the monthly sales tax is simply the monthly lease payment times the tax rate. What APR is the dealer quoting you? (Round your answer to 2 decimal places, (e.g., 32.16)) APR % What is your monthly lease payment for a 36-month lease if the sales tax is 7 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, (e.g., 32.16)) Lease payment $

Explanation / Answer

compute the APR of the loan as follows APR= 2.400 * Factor APR= ( 2400 ) * 0.00271 6.504 Thus, the APR (Annual Percentage Rate) 6.50% calculate the lease payment in the following steps first step Compute net capitalization cost Net Capitalization cost = Base cost + other cost — down payment Net Capitalization cost = 29300 + 900 -3500 Net Capitalization cost =                                   26,700 Thus, the capitalization cost                                   26,700 Second step Compute depreciation charge as follows Depreciation charge = (net capitalization cost — residual value Depreciation charge / number of lease payments =   26700 - 20500 / 36 Depreciation charge = 172.22 Thus, the depreciation charge   172.22 Third step Compute finance charge as follows Finance charge = (net capitalization cost + residual value) x factor Finance charge = (26700 + 20500) x 0.00271 Finance charge = 127.91 Thus, the finance charge 127.91 Fourth step Compute tax as follows Taxes = (depreciation charge + finance charge) x tax rate Taxes = (172.22 + 127.91) x (0.07) Taxes = 21.01 Thus, the amount of tax 21.01 Finally, compute the monthly lease payment as follows Lease payment = Depreciation charge + Finance charge + Tax 172.22 + 127.91 + 21 .01 Lease payment = 321.14 Thus, the lease payment will be $321.14

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