# B Simple Arithmetic Question

#### clearway

Summary
Hello,

I have a simple question and am hoping someone can help. I have a power plant that loses 0.5% production capacity per year for 25 years. When working with the plant capacity in terms of percentages, year 0 is defined as 100% capacity. For year 1 and each subsequent years, is it correct to take the current plant capacity percentage, and multiply it by (100%-0.5%)? Or do I subtract the 0.5% from the previous year?

Plant capacity:
Method 1:
Year 0 = 100%
Year 1 = Year 0 * (100%-0.5%)
Year 2 = Year 1 * (100%-0.5%)
etc

Method 2:
Year 0 = 100%
Year 1 = Year 0 - 0.5%
Year 2 = Year 1 - 0.5%

Thanks.

#### fresh_42

Mentor
2018 Award
Percentage means only "divided by $100$". So $100\%=\frac{100}{100}=1$.

Now Year 1 = Year 0 $\cdot (100\%-0.5\%)=$Year 0 $\cdot (1-\frac{0.5}{100})=$ Year 0 $\cdot 1 -$Year 0 $\cdot \frac{1}{200}$ which is what I think you meant by method 2. However, you haven't said from which quantity you want to take $0.5\%$ in method 2. The methods are the same if you subtract $0.5\%$ from Year 0, which makes sense as you lose this amount already in the first year.

What you also haven't said is, that the losses are cumulative, which your calculation is. For a constant loss you simply have $99.95 \cdot$Total every year.

In year $25$ you will have $\operatorname{capacity}(25)=\operatorname{capacity}(0)\cdot (1-\frac{1}{200})^{25}$ or $24$ if it runs on full capacity the first year.

"Simple Arithmetic Question"

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