You are considering leasing a car. You notice an ad that indicates that you may
ID: 2744740 • Letter: Y
Question
You are considering leasing a car. You notice an ad that indicates that you may lease the car you want for $321.00 per month. The lease term is 60 months with the first payment due at inception of the lease. You must also make an additional down payment of $2060.00. The ad also says that the residual value of the vehicle is $17,966. The total cost of the vehicle based on list price is $28,013, but after much research you have concluded that you could buy the car for a total 'drive-out' price of $25,700. What is the quoted annual interest rate you are actually paying with the lease? Question 20 options: 10.08% 12.85% 10.23% 13.04% 10.52% Save
Explanation / Answer
Answer: 13.04%
Calculation:
The PV of the monthly lease payments + the PV of the residual value + $2060 should equal the drive out price of $25700.
or
The PV of the annual lease payments + the PV of the residual value = $23640
321*pvif of annuity due (i,60) + 17966*pvif(i,60) = 23640
The value of 'i' (the monthly discount rate) has to be found out be trial and error, such that the PV of LHS of the above equation equals $23640.
Starting with 1% per month
PV = 321*45.40 + 17966*0.5504 = 24462
Discounting with 1.25% per month
PV = 321*42.56 + 17966*0.4746 = 22188
exact rate = 1 + 0.25*(24462-23640)/(24462-22188) = 1.09
Annual rate = 1.09*12 = 13.08%. (closest to 13.04%)
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