# inflation rate

• Mar 19th 2007, 05:21 PM
kcsteven
inflation rate
If the inflation rate is 100j% 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 beginniing of that period. this is what I did:

The purchasing power of a dollar at the end of n years of 100% annual inflation is \$1.100^-n or 1 and I know this must be set up inncorrectly. The dollar should be less but I don't think this is the right answer.
Thankx,
Keith
• Mar 19th 2007, 10:08 PM
Soroban
Hello, Keith!

Quote:

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.