# How to calculate the multiplicator in a sum like sum += sum*(mulu^n)

I’ve came with a solution. It gets an approximation of the spending factor because there is no direct formula.

Getting the exact spending factor is too CPU intensive. So, I’m calculating a near approximation first. This value will always be above the solution. I then decrease that number until I’m getting below the total paid amount.

Here is a PHP sample of what I’ve done.

$paymentCount = 4;$initialPayment = 10;
$totalPaid = 1560; //----- precalculate the factor based on total payment for faster computation //----- this predefined factor will always be above our final factor$estimatedSpendingFactor = exp(log($totalPaid) /$paymentCount);

//----- find the estimated spending factor

do
{
$estimatedSpendingFactor -= 0.0001;$y = $initialPayment * (pow($estimatedSpendingFactor, $paymentCount) - 1) / ($estimatedSpendingFactor-1);
}
while ($y >$totalPaid);

//-----

printf("The spending factor is %f\n", \$estimatedSpendingFactor);


the output will be :

The spending factor is : 5.000000