PHP APR Calculation

<?php
// equation derived from explanation on wikipedia.
// by @sweetl80

// 10.2
$term = 35; // duration minus one.
$monthly_payment = 474.19;
$total_credit = 21820.50;
$final_payment = 9873;

$t_apr = 0;
$npv = 0;

// ultimately, these are used for attempting to speed up the calculation with a staged increment system.
$limit[1] = $total_credit * 0.00078;
$limit[2] = $total_credit * 0.00030;
$limit[3] = $total_credit * 0.00010;

while (!$found){
    $npv_perc = round(($npv / $total_credit) * 100,4);

    /*
     * attempting staged increment
     */
    if ($npv_perc >= $limit[1]) $t_apr += 0.01;  // lop off two decimal places (fast increment of apr)
    if ($npv_perc < $limit[1] && $npv_perc >= $limit[2]) $t_apr += 0.001; // add a hundredth. (slower increment)
    if ($npv_perc < $limit[2] && $npv_perc >= $limit[3]) $t_apr += 0.0001; // slower still.
    if ($npv_perc < $limit[3]) $t_apr += 0.00001; // the slowest, for accuracy.

    /*
     * if you dont like the 'staged' setup above, you could just do this instead, but it can lead to hundreds of thousands of calculations
    // $t_apr += 0.00001; // slow, but accurate.
     */

    $npv = -$total_credit;

    for ($m = 1; $m <= $term; $m++){
        if ($m < $term){
            $val = $monthly_payment;
        } else {
            $val = $monthly_payment + $final_payment;
        }

        $npv += ($val / pow(1 + $t_apr,$m/12));
    }

    $loops++;

    if ($npv <= 0){
        $apr = round($t_apr * 100,1);
        break;
    }
}

?>

<h1><?=$apr?> found after <?=$loops?> loops</h1>