Answer:
Assuming the the values for purchase price and lifetime for each bulb, and a cost of electricity are:
Incandescent Bulb
Power:100W
Purchase Price: $1.50
Lifetime: [tex]1000 h \approx 1 year[/tex]
Electricity cost: $0.10/kWh
LED Bulb
Power:20W
Purchase Price: $40
Lifetime: [tex]25000 h \approx 25 years[/tex]
Electricity cost: $0.10/kWh
Let's begin with the calculations:
The electric energy [tex]E[/tex] used for a bulb is:
[tex]E=P.t[/tex] (1)
Where [tex]P[/tex] is the electric power and [tex]t[/tex] the time the bulb is used.
And the operating cost is:
[tex]Cost=E. Cost (/kWh)[/tex] (2)
Where [tex]Cost (/kWh)[/tex] is the Electricity cost in units of [tex]/kWh[/tex]
For the Incandescent Bulb:
[tex]E_{IN}=(100W)(1000h)[/tex] (3)
[tex]E_{IN}=100000 Wh=100 kWh[/tex] (4) This is the electric energy used
Calculating the cost:
[tex]Cost_{IN}=E_{IN} Cost(/kWh)_{IN}[/tex] (5)
[tex]Cost_{IN}=(100 kWh)($0.10/kWh)[/tex] (6)
[tex]Cost_{IN}=\$10[/tex] (7) This is the electricity cost for incandescent light bulb for 1000 hours
For the LED Bulb:
[tex]E_{LED}=(20W)(25000h)[/tex] (8)
[tex]E_{LED}=500000 Wh=500 kWh[/tex] (9) This is the electric energy used by the LED bulb
Calculating the cost:
[tex]Cost_{LED}=E_{LED} Cost(/kWh)_{LED}[/tex] (10)
[tex]Cost_{LED}=(50 kWh)($0.10/kWh)[/tex] (11)
[tex]Cost_{LED}=\$50[/tex] (12) This is the electricity cost for LED bulb for 25000 hours
As we can see the use of LED bulb for 25 years (25000 h) is $50, this means in 1 year the cost would be $2.
On the other hand, the use of Incandescent bulb for 1 year (1000 h) is $10.
This means using the LED bulb will result more cost-effective than the Incandescent bulb, although the initial investment is high.
