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Answer :
Certainly! Here's a step-by-step explanation of how we can find out in how many years the new dryer will pay for itself:
1. Understand the Costs and Savings:
- The old dryer costs [tex]$455 per year to run.
- The new dryer, which costs $[/tex]940 to purchase, will save 18% in energy costs annually.
2. Calculate the Annual Savings:
- First, we need to determine how much money will be saved each year by using the new dryer instead of the old one.
- Calculate the savings by multiplying the cost of running the old dryer by the savings percentage:
[tex]\[
\text{Yearly Savings} = 455 \times 0.18 = 81.90
\][/tex]
- So, you will save approximately [tex]$81.90 each year with the new dryer.
3. Determine How Many Years It Will Take for the New Dryer to Pay for Itself:
- To find out how long it will take for the savings to cover the purchase cost of the new dryer, divide the cost of the new dryer by the annual savings:
\[
\text{Years to Pay Off} = \frac{940}{81.90} \approx 11.48
\]
- This result means it will take about 11.48 years for the savings from the new dryer to pay for its $[/tex]940 cost.
Therefore, the new dryer will pay for itself in a little over 11 years, specifically around 11.48 years.
1. Understand the Costs and Savings:
- The old dryer costs [tex]$455 per year to run.
- The new dryer, which costs $[/tex]940 to purchase, will save 18% in energy costs annually.
2. Calculate the Annual Savings:
- First, we need to determine how much money will be saved each year by using the new dryer instead of the old one.
- Calculate the savings by multiplying the cost of running the old dryer by the savings percentage:
[tex]\[
\text{Yearly Savings} = 455 \times 0.18 = 81.90
\][/tex]
- So, you will save approximately [tex]$81.90 each year with the new dryer.
3. Determine How Many Years It Will Take for the New Dryer to Pay for Itself:
- To find out how long it will take for the savings to cover the purchase cost of the new dryer, divide the cost of the new dryer by the annual savings:
\[
\text{Years to Pay Off} = \frac{940}{81.90} \approx 11.48
\]
- This result means it will take about 11.48 years for the savings from the new dryer to pay for its $[/tex]940 cost.
Therefore, the new dryer will pay for itself in a little over 11 years, specifically around 11.48 years.
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