p%下がった後元に戻すには何%上げればいい?

仮想通貨の取引をしていて気になったので計算してみた。 

0<p<100
(1-p/100)(1+x/100)=1

答えはこの方程式の解でそれは
x=100p/(100-p)

これはpより大きい。
なぜなら
x-p = p^2/(100-p) > 0

 

f(p)=100p/(100-p)

として具体的に数値を代入すると
f( 1 ) = 1.0101010101010102
f( 2 ) = 2.0408163265306123
f( 3 ) = 3.0927835051546393
f( 4 ) = 4.166666666666667
f( 5 ) = 5.2631578947368425
f( 6 ) = 6.382978723404255
f( 7 ) = 7.526881720430108
f( 8 ) = 8.695652173913043
f( 9 ) = 9.89010989010989
f( 10 ) = 11.11111111111111
f( 11 ) = 12.359550561797754
f( 12 ) = 13.636363636363637
f( 13 ) = 14.942528735632184
f( 14 ) = 16.27906976744186
f( 15 ) = 17.647058823529413
f( 16 ) = 19.047619047619047
f( 17 ) = 20.481927710843372
f( 18 ) = 21.951219512195124
f( 19 ) = 23.45679012345679
f( 20 ) = 25.0
f( 21 ) = 26.582278481012658
f( 22 ) = 28.205128205128204
f( 23 ) = 29.87012987012987
f( 24 ) = 31.57894736842105
f( 25 ) = 33.333333333333336
f( 26 ) = 35.13513513513514
f( 27 ) = 36.986301369863014
f( 28 ) = 38.888888888888886
f( 29 ) = 40.84507042253521
f( 30 ) = 42.857142857142854
f( 31 ) = 44.927536231884055
f( 32 ) = 47.05882352941177
f( 33 ) = 49.25373134328358
f( 34 ) = 51.515151515151516
f( 35 ) = 53.84615384615385
f( 36 ) = 56.25
f( 37 ) = 58.73015873015873
f( 38 ) = 61.29032258064516
f( 39 ) = 63.9344262295082
f( 40 ) = 66.66666666666667
f( 41 ) = 69.49152542372882
f( 42 ) = 72.41379310344827
f( 43 ) = 75.43859649122807
f( 44 ) = 78.57142857142857
f( 45 ) = 81.81818181818181
f( 46 ) = 85.18518518518519
f( 47 ) = 88.67924528301887
f( 48 ) = 92.3076923076923
f( 49 ) = 96.07843137254902
f( 50 ) = 100.0
f( 51 ) = 104.08163265306122
f( 52 ) = 108.33333333333333
f( 53 ) = 112.76595744680851
f( 54 ) = 117.3913043478261
f( 55 ) = 122.22222222222223
f( 56 ) = 127.27272727272727
f( 57 ) = 132.5581395348837
f( 58 ) = 138.0952380952381
f( 59 ) = 143.90243902439025
f( 60 ) = 150.0
f( 61 ) = 156.4102564102564
f( 62 ) = 163.1578947368421
f( 63 ) = 170.27027027027026
f( 64 ) = 177.77777777777777
f( 65 ) = 185.71428571428572
f( 66 ) = 194.11764705882354
f( 67 ) = 203.03030303030303
f( 68 ) = 212.5
f( 69 ) = 222.58064516129033
f( 70 ) = 233.33333333333334
f( 71 ) = 244.82758620689654
f( 72 ) = 257.14285714285717
f( 73 ) = 270.3703703703704
f( 74 ) = 284.61538461538464
f( 75 ) = 300.0
f( 76 ) = 316.6666666666667
f( 77 ) = 334.7826086956522
f( 78 ) = 354.54545454545456
f( 79 ) = 376.1904761904762
f( 80 ) = 400.0
f( 81 ) = 426.3157894736842
f( 82 ) = 455.55555555555554
f( 83 ) = 488.2352941176471
f( 84 ) = 525.0
f( 85 ) = 566.6666666666666
f( 86 ) = 614.2857142857143
f( 87 ) = 669.2307692307693
f( 88 ) = 733.3333333333334
f( 89 ) = 809.0909090909091
f( 90 ) = 900.0
f( 91 ) = 1011.1111111111111
f( 92 ) = 1150.0
f( 93 ) = 1328.5714285714287
f( 94 ) = 1566.6666666666667
f( 95 ) = 1900.0
f( 96 ) = 2400.0
f( 97 ) = 3233.3333333333335
f( 98 ) = 4900.0
f( 99 ) = 9900.0

となる。

 

コイン単価が50万のときに買って10%下がって45万になったところで損切りして40万で買い戻したら損が0になるには40万*f(10) = 44万4444円にならなければならないってことか。