You recently purchased a twin-engine plane after landing an ultra-lucrative job on Wall Street. The annual payments on the plane are $8,000 per year and the installment plan extends over 5 years. The payments start today. If your discount rate is 8.5% per year, how much would it have cost you to purchase the plane on an all-cash basis?
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A. B. C. D.A
The present value of the installment payments equals 8,000 + (8,000/0.085)*(1-1/(1.085^4)) = $34,205
To determine the cost of purchasing the plane on an all-cash basis, we need to calculate the present value of the annual payments at a discount rate of 8.5% per year.
The formula to calculate the present value of an annuity is:
PV = PMT × [(1 - (1 + r)^(-n)) / r],
where PV is the present value, PMT is the annual payment, r is the discount rate, and n is the number of years.
Given that the annual payments on the plane are $8,000 per year and the installment plan extends over 5 years, we can substitute these values into the formula:
PV = $8,000 × [(1 - (1 + 0.085)^(-5)) / 0.085].
Let's calculate the present value:
PV = $8,000 × [(1 - (1.085)^(-5)) / 0.085] = $8,000 × [(1 - 0.58079) / 0.085] = $8,000 × (0.41921 / 0.085) = $8,000 × 4.92847 = $39,427.76.
Therefore, the cost of purchasing the plane on an all-cash basis would be approximately $39,427.76.
Among the given answer choices, the closest option is:
B. $40,611.
Please note that the answer may vary slightly due to rounding differences or if a different method of rounding is used in the calculation.