Summary

DescriptionFractional-reserve-banking base100 0.8reserve rate.svg	English: Illustration of the en:fractional reserve lending with a 20% reserve rate Deutsch: Illustration der de:Giralgeldschöpfung mit einer de:Mindestreserve von 20%
Date	28 January 2014, 22:35:47
Source	Own work
Author	Erik Streb
Other versions

Equation and Gnuplot source

${\displaystyle \sum _{n=0}^{k}gr^{n}=g{\frac {r^{k+1}-1}{r-1}}}$, where ${\displaystyle k}$ is the number of individual deposits, ${\displaystyle r}$ is the reserve rate and ${\displaystyle g}$ is the initially deposited value.

set term svg size 800, 480 font "DejaVu Sans,16"
set output "fractional-reserve-banking___base100___0.8reserve_rate.svg"

set samples 10000

set title "The Expanson of $100 Through Fractional-Resverve\nLending with a 20 % Reserve Rate"
set xlabel "Individual Deposits"
set ylabel "Total Amount of Deposited Money"

set style line 1 lc rgb '#006600' lt 1 lw 2 # --- green
set style line 11 lc rgb '#808080' lt 1
set border 3 back ls 11
set tics nomirror
set style line 12 lc rgb '#808080' lt 0 lw 1
set grid back ls 12
set style fill transparent solid 0.8 noborder
set nokey

set xtics ("A" 0, "B" 1, "C" 2, "D" 3, "E" 4, "F" 5, "G" 6, "H" 7, "I" 8, "J" 9, "K" 10, "L" 11, "M" 12, "N" 13, "O" 14, "P" 15, "Q" 16, "R" 17, "S" 18, "T" 19, "U" 20, "V" 21, "W" 22, "X" 23, "Y" 24, "Z" 25)
set ytics ("$0" 0, "$100" 100, "$200" 200, "$300" 300, "$400" 400, "$500" 500)

g=100 # base value
r=0.8 # reserve rate

plot [0:25] [0:500] g*(r**(x+1)-1)/(r-1) ls 1 w filledcurves x1

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