Question

A local car dealer is advertising two leasing options for its new XT 3000 series sports car.

**Option A**: is a
standard 24-month lease of $1150 per month. In addition, this
option requires a down payment of $4100, plus a $1100 refundable
initial deposit. In option A, the lease payments are due at the
beginning of every month. For example, the first lease payment
(equal to $1150) is due at the beginning of month 1.

**Option B**: In this
option, the company offers a 24-month lease plan that has only a
single up-front payment of $31000 (which is paid at the beginning
of month one)

**Note**: The initial
deposit in option A will be refunded to the customer at the end of
month 24.

Assume an interest rate of 15.4% compounded monthly. Which option is better for the customer? Use present worth method.

SHOW ALL WORK

Answer #1

i = 15.4% / 12 = 1.28333% per month

NPW of option 1 = -(4100+1100+1150) - 1150*(P/A,1.28333%,23) + 1100*(P/F,1.28333%,24)

= -(4100+1100+1150) - 1150*(((1 + 0.0128333)^23-1)/(0.0128333 * (1 + 0.0128333)^23)) + 1100*((1 + 0.0128333)^-24)

= -(4100+1100+1150) - 1150*(((1.0128333)^23-1)/(0.0128333 * (1.0128333)^23)) + 1100*((1.0128333)^-24)

= -(4100+1100+1150) - 1150*19.8072719 + 1100* 0.73635744

= -28318.369

NPW of option B = -31000

As present cost of option 1 is lower, it should be selected

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