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A car may be leased for 4 years from a dealer with $330 monthly lease payments...

A car may be leased for 4 years from a dealer with $330 monthly lease payments to be paid at the beginning of each month. At the end of the lease, the car has a residual value of  $23,000. If the dealer is charging interest at 2% compounded monthly, what is the implied cash price of the vehicle. Assume no down payment is m

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Answer #1

Implied cash price of the car is the present value of monthly payments and the residual value.

Effective monthly rate, r = 2%/12 = 0.001666666667

Number of monthly payments, n = 4 * 12 = 48

PV of the monthly payments with first payment is made immediately.

PV of the residual value

PV = FV/(1 + r)^n

PV = 23,000/(1 + 0.001666666667)^48

PV = $21,233.0898879423

Implied cash price of the car = 15,236.1427163785 + 21,233.0898879423

Implied cash price of the car = $36,469.2326043208

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