A 2,000 square foot house in New Jersey costs $1,800 each winter to heat with it

Question

A 2,000 square foot house in New Jersey costs $1,800 each winter to heat with its existing oil-burning furnace. For an investment of $5,500, a natural gas furnace can be installed, and the winter heating bill is estimated to be $1, 200. If the homeowner's MARR is 8% per year, what is the discounted payback period of this proposed investment? Choose the correct answer below. A. The discounted payback period of this proposed investment is 18 years. B. The discounted payback period of this proposed investment is 10 years. C. The discounted payback period of this proposed investment is 12 years. D. The discounted payback period of this proposed investment is 11 years.

Explanation / Answer

Total Amount = $5,500

Each Payment P= Difference in cost = $1800 - $1200 = $600

r = 8%

Total Amount = P[ 1 - (1+r)^-n)/r)

$5,500 = 600(1 - (1+0.08)^-n)/0.08

5500*(0.08/600) = 1 - 1.08^-n

0.733 = 1 - 1.08^-n

  1.08^-n = 0.266

1.08^n = 1/0.266 = 3.76

Taking log on both sides

nlog1.08 = log3.76

n = log3.76/log1.08

n = 18 years

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