Question

Automobiles are often leased, and there are several terms unique to auto leases. Suppose you are considering leasing a car. The price you and the dealer agree on for the car is $27,600. This is the base capitalized cost. Other costs that may be added to the capitalized cost price include the acquisition (bank) fee, insurance, or extended warranty. Assume these costs are $1,050. Capitalized cost reductions include any down payment, credit for a trade-in, or dealer rebate. Assume you make a down payment of $3,000 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 $17,000 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 .00265. 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 the depreciation payment plus the finance fee, times the tax rate.

a. What APR is the dealer quoting you? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b. 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.)

Answer 1

a. 6.36%

b. $378.02

Explanation:

a. The computation of Annual percentage rate is shown below:-

Annual percentage rate = Lease factor × 2,400

= 0.00265 × 2,400

= 6.36%

b. For computation of monthly lease payment first we need to find out the depreciation charge, finance charge and tax which is shown below:-

Depreciation charge = (Base cost + Other cost - Down payment - Residual value) ÷ Number of lease payment

= ($27,600 + $1,050 - $3,000 - $17,000) ÷ 36

= $8,650 ÷ 36

= $240.27

Finance charge = (Base cost + Other cost - Down payment - Residual value) × Lease factor

= ($27,600 + $1,050 - $3,000 - $17,000) × 0.00265

= $42,650 × 0.00265

= $113.0225

now,

Tax = (Depreciation charge + Finance charge) × Tax rate

= ($240.27 + $113.0225) × 7%

= $353.2925 × 7%

= $24.73

Monthly Lease payment = Depreciation charge + Finance charge + Tax

= $240.27 + $113.0225 + $24.73

= $378.02