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Suppose the purchase price of a bulldozer is $90,000,its residual value in four years is certain to be $15,000,and there is no risk that the lessee will default on the lease.Assume that capital markets are perfect and the risk-free interest rate is 6% APR with monthly compounding.
-The monthly lease payments for a four-year lease of the bulldozer are closest to:
A)$1870.
B)$1825.
C)$1750.
D)$2115.

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the residual value at the end of the lease term. Using the formula:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.
PV of residual value = $15,000 / (1 + 0.06/12)^48 = $9,238.45

Next, we can use the formula for the present value of an annuity to calculate the monthly lease payment:
PV = PMT x [(1 - (1 + r)^-n) / r]
where PV is the present value, PMT is the monthly payment, r is the interest rate per period, and n is the number of periods.
PV of lease payments = $90,000 - $9,238.45 = $80,761.55
PMT = $80,761.55 / [(1 - (1 + 0.06/12)^-48) / (0.06/12)] = $1,825.55, which rounded to the nearest dollar is $1,825.
Therefore, the closest answer choice is B) $1825.

Use the Information for the Question(s)below