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 $$49,500.$ This is the base capitalized cost. Other costs added to the capitalized cost price include the acquisition $($bank$)$ fee, insurance, or extended warranty. Assume these costs are $$850.$ Capitalization cost reductions include any down payment, credit for trade$-$in$,$ or dealer rebate. Assume you make a down payment of $$5,000,$ and there is no trade$-$in or rebate. If you drive $10,000$ miles per year, the lease$-$end residual value for this car will be $$28,500$ 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 money factor of $2,400$ is the product of three numbers: $2,12,$ and $100.$ The $100$ is used to convert the APR, expressed as a percentage, to a decimal number. The $12$ converts this rate to a monthly rate. Finally, the monthly rate is applied to the sum of the net capitalization cost plus the residual. If we divide this sum by $2,$ the result is the average anticipated book value. Thus, the end result of the calculation using the money factor is to multiply a monthly rate by the average book value to get a monthly payment. The lease factor the dealer quotes you is $\mathrm{.}00185.$

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$.,32\mathrm{.}16.)$

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$.,32\mathrm{.}16.)$