Hyperinflation - Units of Inflation

Units of Inflation

Inflation rate is usually measured in percent per year. It can also be measured in percent per month or in price doubling time.

Example of inflation rates and units
When first bought, an item cost 1 currency unit. Later, the price rose...
Old price New price 1 year later New price 10 years later New price 100 years later (Annual) inflation Monthly
inflation
 Price
doubling
time
 Zero add time
1
1 .0001
1 .001
1 .01
0.01
0 .0008
6931
23028
1
1 .001
1 .01
1 .11
0.1
0 .00833
693
2300
1
1 .003
1 .03
1 .35
0.3
0 .0250
231
769
1
1 .01
1 .10
2 .70
1
0 .0830
69 .7
231
1
1 .03
1 .34
19 .2
3
0 .247
23 .4
77.9
1
1 .1
2 .59
13800
10
0 .797
7 .27
24.1
1
2
1024
1.27 × 1030
100
5 .95
1
3.32
1
10
1010
10100
900
21 .2
0 .301 (3⅔ months)
1
1
31
8.20 × 1014
1.37 × 10149
3000
32 .8
0 .202 (2½ months)
0.671 (8 months)
1
1012
10120
101,200
1014
900
0 .0251 (9 days)
0.0833 (1 month)
1
1.67 × 1073
1.69 × 10732
1.87 × 107,322
1.67 × 1075
1.26 × 108
0 .00411 (36 hours)
0.0137 (5 days)
1
1.05 × 102,637
1.69 × 1026,370
1.89 × 10263,702
1.05 × 102,639
5.65 × 10221
0 .000114 (1 hour)
0.000379 (3.3 hours)

\hbox{New price } y \hbox{ years later} = \hbox{old price } \times \left(1+\frac{\hbox{inflation}}{100}\right)^{y}

\hbox{Monthly inflation } = 100 \times \left(\left(1+\frac{\hbox{inflation}}{100}\right)^{\frac{1}{12}} -1\right)

\hbox{Price doubling time} = \frac{\log_{e} 2}{\log_{e} \left(1+ \frac{\hbox{inflation}}{100}\right)}

\hbox{Years per added zero of the price } = \frac{1}{\log_{e} \left(1+ \frac{\hbox{inflation}}{100}\right)}

Often, at redenominations, three zeroes are cut from the bills. It can be read from the table that if the (annual) inflation is for example 100%, it takes 3.32 years to produce one more zero on the price tags, or 3 × 3.32 = 9.96 years to produce three zeroes. Thus can one expect a redenomination to take place about 9.96 years after the currency was introduced.

Read more about this topic:  Hyperinflation

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