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# linear interpolation of the capital recovery factor

The Biltmore Garage has lights in places that are difficult to reach. Management estimates that it costs about \$2 to change a bulb. Standard 100-watt bulbs with an expected life of 1000 hours are now used. Standard bulbs cost \$1. A long-life bulb that requres 90 watts for the same effective level of light is available. Long-life bulbs cost \$3. The bulbs that are difficult to reach are in use for about 500 hours a month. Electricity costs \$0.08/kilowatt-hour payable at the end of each month. Biltmore uses a 12% MARR (1% per month) for projects involving supplies.

a) What minimum life for the long-life bulb would make its cost lower?

b) If the cost of changing bulbs is ignored, what is the minimum life for the long-life bulb for them to have a lower cost?

c) If the solutions are obtained by linear interpolation of the capital recovery factor, will the approximations understate or overstate the required life?

If you use Excel, please transfer all results to a Word file, but include both files. Thanks.

#### Solution Summary

Linear interpolation of the capital recovery factor is emphasized.

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