It seems hard to justify spending $5 for a compact fluorescent lightbulb when an

Question

It seems hard to justify spending $5 for a compact fluorescent lightbulb when an ordinary incandescent lightbulb costs 50 cents. To see if this makes sense, compare a 60 W incandescent bulb lasting 1000 hours to a 15 W compact fluorescent bulb having a lifetime of 10,000 hours. Both bulbs produce the same amount of visible light and are interchangeable. If electricity costs 0.10 dollars/kWh, what is the cost - purchase plus energy - to obtain 10,000 hours of light from each type of bulb? This is called the life-cycle cost.

A)Life-cyle cost ($) of incandescent blub?

B)Life-cyle cost ($) of fluorescent blub?

Explanation / Answer

First, find out how much energy the incandescent bulbs use:

(60 watts) x (1000 hours) = (60,000 watt hours)

60,000 watt hours (Wh) = 60 kilowatt hours (kWh)

Now, figure how much it costs for the energy. You know how many hours the bulb runs, and you know the cost per hour, so...

(60 kWh) x ($0.10/kWh) = ($6.00)

However, you need to add the cost of the bulb, since it doesn't just appear out of nowhere. You DO have to buy them.

$6.00 + $0.50 = $6.50

So, every incandescent bulb costs $6.50 per 1000 hours, energy included.

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Now, you need to do the same thing for the fluorescent bulbs. Calculate the amount of energy consumed by these bulbs.

(15 watts) x (10,000 hours) = (150,000 watt hours)

150,000 watt hours (Wh) = 150 kilowatt hours (kWh)

Once again, it's time to figure how much it costs for the energy. You know how many hours the bulb runs, and you know the cost per hour, so...

(150 kWh) x ($0.10/kWh) = ($15.00)

Once again, add the price of the bulb into the total cost.

$15.00 + $5.00 = $20.00

So, over the course of 10,000 hours, the total cost of the fluorescent bulb is $20.00.

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Now, time to add up all of the total costs. First, compare the two bulb prices.

Incandescent: $6.50/1,000 hours
Fluorescent: $20.00/10,000 hours

At first glance, it appears as if the Incandescent bulb is much cheaper. However, you need to convert the incandescent into the same time frame as the fluorescent. The incandescent costs $6.50 per 1000 hours. But, you need 10 incandescents to match the time frame of the flourescent. So:

($6.50 per 1,000 hours) x (10) = ($65.00 per 10,000 hours)

Now, compare the costs.

Incandescent: $65.00/10,000 hours
Fluorescent: $20.00/10,000 hours

Over the course of 10,000 hours, it is clear that the fluorescent is the cheaper of the two. By purchasing fluorescent bulbs, you are saving 45 dollars, with every bulb.

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