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Mysteries of Percents

Suppose inflation was 11% last year, and 11% this year. Is that a total inflation of 22% for the two years?

Consider a sample of purchases costing $100. After the first year, 11% inflation means you will pay 11% more for the same items.

11% of $100 is $11. Therefore, you will pay $111 by the end of the year for those same items.

In the second year, another 11% inflation assaults your pocketbook. By the end of the second year, you will pay 11% more on $111.

11% of $111 is $12.21. Therefore, by the end of the second year, you will pay $111 + $12.21 = $123.21 for the same goods.

So after two years, you are paying an additional $23.21, or 23.21% more for those same items, which is higher than 22%.

This is because percent increase (or percent decrease) is exponential, and not linear. Exponential growth is what grows your savings account over the years, and what allows inflation to eat it away.

Note that the longer the time period, the bigger the difference between the exponential and the linear value.

For instance, suppose there was 11% inflation for 10 years. What would the price of your $100 basket of goods be?

Using the exponential equation, we have

$100(1 + 0.11)^10 = $283.94

That’s a 283% increase!

Can you figure?: If you lost 5% of your weight one year, and then lost another 5% the next year, would you have lost a total of 10% of your original weight?

There are many confusions related to percents because of this principle of exponential growth. For instance, suppose you had investments totaling $1000 and during a market downturn, you lost 30% of that investment.

30% of $1000 is $300, so your investments are now worth $1000 – $300 = $700.

Now, suppose the market goes back up 30%. Are you back to your original investment value of $1000?

No! 30% of $700 is $210. Adding $700 + $210 = $910. You are still down $90.

$300 is approximately 43% of $700. So to increase your $700 back up to $1000, there would have to be a 43% increase in the market!

Can you figure?: If you lost 20% in the stock market, what percent would the market need to increase to recoup your loss?

Such is the mysterious way of percents.