If the inflation rate is 100% per annum over a period of n years,
what is the purchasing power of a dollar at the end of n years
as a percentage of its purchasing power at the beginning of that period?
I worked out the math behind this problem,
. . but here's a baby-talk explanation.
If the inflation is 100% per year,
. . then an item costing $1 this year will cost $2 next year,
. . and $4 the next year, then $8 the next year . . .
In other words, the purchasing power is cut in half every year . . .
. . to ½ the first year, to ¼ the second year, etc.
At the end of the nth year, $1 will be worth only 1/(2^n) dollars.
As a percentage, the purchasing power is 100/(2^n) percent.