SOLUTION: Does anyone know how to answer this question? I do not understand it. Thank you. If prices increase 2% each year for 10 years, then a jacket that costs $90 today will cost $109.

Question 1139393: Does anyone know how to answer this question? I do not understand it. Thank you.
If prices increase 2% each year for 10 years, then a jacket that costs $90 today will cost $109.71 in 10 years. What is the percentage decrease in the buying power of currency over the 10-year period?
Found 3 solutions by MathLover1, Theo, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
If prices increase % each year for years, then a jacket that costs $ today will cost $ in years.
here is how:
Start amount: $
After year:
After years:
After years:
etc
so after 10 years:
the difference in prices or price increase was:

and find what is it of the price

so its percent increase is %
=> percent increase in price= percent decrease in the buying power of currency

in your case, decrease in the buying power of currency over the 10-year period will be: %
remember:
decrease in the buying power of currency- simply, inflation
the impact that inflation has on the time value of money is it decreases the value of a dollar over time
inflation increases the prices of goods and services over time, effectively decreasing the amount of goods and services you can buy with a dollar in the future as opposed to a dollar today

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
if the price of the jacket is 90 dollars today and inflation is 2% per year, then the price of the jacket in 10 years will be 1.02 ^ 10 * 90 = 109.7094978 dollars.

your 90 dollars buys 100% of the price of the jacket today.

your same 90 dollars can only buy 90 / 109.7094978 = .8203482999 * 100 = 82.03482999% of the price of the jacket 10 years from now.

that's a drop in buying power from 100% to 82.03482999% = 17.96517001%.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

The solution by tutor MathLover1 is not correct.

After finding that the percent increase in price is 21.9%, she incorrectly states

"=> percent increase in price= percent decrease in the buying power of currency"

which is not correct. As a simple way to see this, suppose the price was doubled, making the increase in price 100%. Would your buying power be decreased by 100%?

Of course not. If the price has doubled, your buying power has decreased by 50%, not 100%.

So if you are going to solve the problem the way she started, you need to say your buying power has been reduced by a factor of 100/121.9 = 0.8203. So the decrease in your buying power is 1-0.8203, which converted to a percentage is 17.97%.

ANSWER: The percentage decrease in buying power over the ten years is 17.97%.
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