PHP implementation of PayPal fee calculator

feecalc.php

<?php
/// Start of a PayPal fee calculator that I'll probably never finish. :-[

/*
Given:
total(cost, fee) := cost + fee(cost)
fee(cost) := F + P*cost
F := $0.30
P := 2.9%


Find:
Total amount to charge so that the customer pays all fees.

paid - fees >= cost
fees := fee(paid) = F + P*paid

paid - (F + P - paid)
paid*(1-P) - F >= cost
paid >= (cost + F)/(1-P)
*/


/**
 * Calculates the total amount to charge based a customer based on a given
 * sub-total amount.
 */
function total($subtotal, $fees)
{
    // total := subtotal + fees
    return bcadd($subtotal, $fees($subtotal));
}

function paypal_fees($subtotal, $flat_fee = "0.30", $variable_rate = "0.029")
{
    // fees := F + P * subtotal

    // subtotal + F
}