#!/usr/bin/perl -W

sub f {
    my $i = shift;
    return $capital - $cuota * (1-(1+$i)**(-$n)) / $i;
}

$capital = 400_000;
$n = 30*12;
$cuota = 2200;

$EPS=1;
while (1+$EPS > 1){
    $EPS /= 2;
}

$a = 2*$EPS;        # strictly >0
$b = 1;         # could be a bigger number, 1 == 100%

while (++$count < 1000 && $a ne $b){
    $m = ($a+$b)/2;
    $max = f($a);
    $min = f($b);
    $mean = f($m);
    print "$count)  $max  $min\n";
    print "$a $b  mean $m\n";
    print "error= $mean\n";
    if ($max*$mean<0){
	$b=$m;
    }elsif ($mean*$min<0){
	$a=$m;
    }elsif (abs($max-$min)<=$EPS || $max eq $min){
	last;
    }
}
print "TAE = ", ((1+$m)**12)-1, "\n";  # annualized

__END__

This is a mortage data, to solve for interest rate of the pay period 
(iterative bisection method)