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.

Algebra ->  Distributive-associative-commutative-properties -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
If prices increase 2% each year for 10 years, then a jacket that costs $90 today will cost $109.71 in 10+years.
here is how:
Start amount: $90
After 1 year: 1.02%2890%29
After 2+years:+1.02%281.02%2890%29%29
After 3 years: 1.02%281.02%281.02%2890%29%29%29
etc
so after 10 years: 1.02%5E10+%2A+90+=+109.7094977=109.71
the difference in prices or price increase was:
109.71-90=19.71
and find what percentage is it of the original price
%28x%2F100%2990=19.71
9x%2F10=19.71
9x=19.71%2A10
x=197.1%2F9
x=21.9
so its percent increase is 21.9%
=> 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: 21.9%
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) About Me  (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) About Me  (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%.