Determinação da taxa de juro composto

# usado no artigo do Quora https://bit.ly/quora-taxa-de-juros

  c=100000.00  # capital inicial
  a=1000.00    # aporte periódico
  m=1000000.00 # montante final
  t=120        # tempo de aplicação
# i=?          # taxa de juros

find-i()
{
  local usar prec i args f d
  eval $@
  if [[ ! ( $usar && $prec && $i ) ]]
  then
    args='usar=<m|t> prec=<#dígitos> i=<chute em %>'
    echo Uso: $FUNCNAME $args >&2
    return 1
  fi
  case $usar in
  m) f='(c*i+a)*(1+i)^t-a-m*i'
     d='(i+1)^(t-1)*(a*t+c*(t+1)*i+c)-m'
     ;;
  t) f='t*l(i+1)-l(m*i+a)+l(c*i+a)'
     d='t/(i+1)-m/(m*i+a)+c/(c*i+a)'
     ;;
  *) echo fórmula desconhecida >&2; return 2
  esac
  BC_LINE_LENGTH=0 bc -l << EOT
  m=$m; c=$c; a=$a; t=$t; p=$prec; i=$i
  define f(i){return $f}
  define d(i){return $d}
  define a(n){if(n>0)return n else return -n}
  n=0
  diff=1
  print "\ni0 = ", i, "\n"
  i=i/100
  while( diff > 10^-p )
  {
    scale=p+2
    i0=i
    i=i0-f(i0)/d(i0)
    diff=100*a(i0-i)
    n+=1
    scale=p
    print "i", n, " = ", 100*i/1, \
          "  |i", n, "-i", n-1, "| = ", diff/1, "\n"
  }
  print "\ni = ", 100*i/1, " %\nm = ", \
        ( (c*i+a)*(1+i)^t - a )/i, "\n\n"
EOT
}

find-i usar=m prec=5 i=1