percentage decrease in the buying power of a dollar

Question

Suppose the rate of inflation this year is 3%. What is the percentage decrease in the buying power of a dollar? Round your answer to the nearest tenth of a percent.

Answer 1

if inflation is 3% this past year

the percent of decrease in the buying power of the dollar is not also 3%1

if inflation were 100%, a 100% decrease in the buying power of the dollar would mean the dollar was worthless, but it's not as prices doubled and purchasing power is half what it used to be, with a 50% decrease in purchasing power 100% inflation meant you once could buy $100 worth of a product but now can only buy 1/1+1 = 1/2 = 50% as much

3% inflation means 1 - 1/1.03 = about .029 = about 2.9% reduction in purchasing power

say the price of a product were $100. with 3% inflation it now costs $103

the $100 now only buys 100/103 worth of the product

the purchasing power went from 100/100 to 100/103 = 1- 100/103 = .02912621359 = 2.912621359 % reduction in purchasing power = about 2.9% decrease