Editing Hyperinflation (section)

==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.

<!-- TABLES NOTE: "Unfortunately, the only way to align columns of numbers at the decimal point is to use two columns, with the first right-justified and the second left-justified." This can be confusing. For example, ... | 1 || ...| .001 below is correct because it displays together as 1.001. See [[Help:Table#Decimal point alignment]] -->
{|class="wikitable" style="text-align:right"
|+'''Example of inflation rates and units'''<br />When first bought, an item cost 1 currency unit. Later, the price rose...
|- style="background:#ececec;"
! style="text-align:center;"| Old price !! style="text-align:center;"| New price 1 year later !! style="text-align:center;"| New price 10 years later !! style="text-align:center;"| New price 100 years later !! style="background:#dcfcdc; text-align:center;"| (Annual) inflation [%] !! style="text-align:center;"| Monthly<br />inflation<br />[%] !! style="text-align:center;"| Price<br />doubling<br />time<br />[years] !! style="text-align:center;"| Zero add time [years]
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .0001
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .001
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .01
|}
| style="background:#f7fcf7;"| '''0.01''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 0 || style="text-align:left; width:40px;"| .0008
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 6931 || style="text-align:left; width:120px;"|
|}
|23028
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .001
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .01
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .11
|}
| style="background:#f7fcf7;"| '''0.1''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 0 || style="text-align:left; width:40px;"| .00833
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 693 || style="text-align:left; width:120px;"|
|}
|2300
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .003
|}
|
{| cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .03
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .35
|}
| style="background:#f7fcf7;"| '''0.3''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 0 || style="text-align:left; width:40px;"| .0250
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 231 || style="text-align:left; width:120px;"|
|}
|769
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .01
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .10
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 2 || style="text-align:left; width:40px;"| .70
|}
| style="background:#f7fcf7;"| '''1''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 0 || style="text-align:left; width:40px;"| .0830
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 69 || style="text-align:left; width:120px;"| .7
|}
|231
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .03
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .34
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 19 || style="text-align:left; width:40px;"| .2
|}
| style="background:#f7fcf7;"| '''3''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 0 || style="text-align:left; width:40px;"| .247
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 23 || style="text-align:left; width:120px;"| .4
|}
|77.9
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1 || style="text-align:left; width:40px;"| .1
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 2 || style="text-align:left; width:40px;"| .59
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 13800 || style="text-align:left; width:40px;"|
|}
| style="background:#f7fcf7;"| '''10''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 0 || style="text-align:left; width:40px;"| .797
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 7 || style="text-align:left; width:120px;"| .27
|}
|24.1
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 2 || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1024 || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.27 × 10<sup>30</sup> || style="text-align:left; width:40px;"|
|}
| style="background:#f7fcf7;"| '''100''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 5 || style="text-align:left; width:40px;"| .95
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 1 || style="text-align:left; width:120px;"|
|}
|3.32
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 10 || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 10<sup>10</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 10<sup>100</sup> || style="text-align:left; width:40px;"|
|}
| style="background:#f7fcf7;"| '''900''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 21 || style="text-align:left; width:40px;"| .2
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 0 || style="text-align:left; width:120px;"| .301 ''({{frac|3|2|3}} months)''
|}
|1
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 31 || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 8.20 × 10<sup>14</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.37 × 10<sup>149</sup> || style="text-align:left; width:40px;"|
|}
| style="background:#f7fcf7;"| '''3000''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 32 || style="text-align:left; width:40px;"| .8
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 0 || style="text-align:left; width:120px;"| .202 ''({{frac|2|1|2}} months)''
|}
|0.671 ''(8 months)''
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 129.7463 || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.35 × 10<sup>21</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 2.04 × 10<sup>211</sup> || style="text-align:left; width:40px;"|
|}
| style="background:#f7fcf7;"| '''12874.63''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 50 || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 0 || style="text-align:left; width:120px;"| .1424 ''(52 days)''
|}
|0.4732 ''({{frac|5|2|3}} months)''
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 10<sup>12</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 10<sup>120</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 10<sup>1,200</sup> || style="text-align:left; width:40px;"|
|}
| style="background:#f7fcf7;"| '''10<sup>14</sup>''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 900 || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 0 || style="text-align:left; width:120px;"| .0251 ''(9 days)''
|}
|0.0833 ''(1 month)''
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.67 × 10<sup>73</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.69 × 10<sup>732</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.87 × 10<sup>7,322</sup> || style="text-align:left; width:40px;"|
|}
| style="background:#f7fcf7;"| '''1.67 × 10<sup>75</sup>''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.26 × 10<sup>8</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 0 || style="text-align:left; width:120px;"| .00411 ''(36 hours)''
|}
|0.0137 ''(5 days)''
|-
|1 ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.05 × 10<sup>2,637</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.69 × 10<sup>26,370</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 1.89 × 10<sup>263,702</sup> || style="text-align:left; width:40px;"|
|}
| style="background:#f7fcf7;"| '''1.05 × 10<sup>2,639</sup>''' ||
{|cellpadding="0" cellspacing="0" style="width:120px;"
|-
| style="text-align:right; width:80px;"| 5.65 × 10<sup>221</sup> || style="text-align:left; width:40px;"|
|}
|
{|cellpadding="0" cellspacing="0" style="width:150px;"
|-
| style="text-align:right; width:30px;"| 0 || style="text-align:left; width:120px;"| .000114 ''(1 hour)''
|}
|0.000379 ''(3.3 hours)''
|-
|}

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

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

<math>\hbox{Price doubling time} = \frac{1}{\log_2 \left(1+ \frac{\hbox{inflation}}{100}\right)}</math>

<math>\hbox{Years per added zero of the price} = \frac{1}{\log_{10} \left(1+ \frac{\hbox{inflation}}{100}\right)}</math>

Often, at [[redenomination]]s, three zeros are cut from the face values of denominations. It can be read from the table that if the (annual) inflation is for example 100%, it takes about 3.32 years for prices to increase by an [[order of magnitude]] (e.g., to produce one more zero on the price tags), or 9.97 years to produce three zeros. Thus can one expect a redenomination to take place about ten years after the currency was introduced.