It costs $27,000 to retrofit the gasoline pumps at a certain filling station so

Question

It costs $27,000 to retrofit the gasoline pumps at a certain filling station so the pumps can dispense E85 fuel (85% ethanol and 15% gasoline)· lf the station makes a profit of $0.07 per gallon from selling E85 and sells an average of 22,000 gallons of E85 per month, how many months will it take for the owner to recoup her $27,000 investment in the retrofitted pumps? The interest rate is 2% per month. Click the icon to view the interest and annuity table for discrete compounding when i#2% per month. t will takemonths to recoup the investment. (Round up to the nearest whole number.)

Explanation / Answer

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Initial cost 27000 No. of gallons sold per month 22000 Profit per gallon 0.07 Therefore profit per month 1400 Interest rate = 2% per month the no. of month required to recop the investment   = 27000    =      1400 * PVAF(2% , n ) PVAF (2% , n ) =    27000 /1400 PVAF (2% , n ) =   19.28571 Therefore n = 24.5 months Here the value is in between 24 and 25th month so we take answer between these PVAF Table to find n Month PVF@2% Cumulative 1 0.980392 0.980392 2 0.961169 1.941561 3 0.942322 2.883883 4 0.923845 3.807729 5 0.905731 4.71346 6 0.887971 5.601431 7 0.87056 6.471991 8 0.85349 7.325481 9 0.836755 8.162237 10 0.820348 8.982585 11 0.804263 9.786848 12 0.788493 10.57534 13 0.773033 11.34837 14 0.757875 12.10625 15 0.743015 12.84926 16 0.728446 13.57771 17 0.714163 14.29187 18 0.700159 14.99203 19 0.686431 15.67846 20 0.672971 16.35143 21 0.659776 17.01121 22 0.646839 17.65805 23 0.634156 18.2922 24 0.621721 18.91393 25 0.609531 19.52346

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