multidimensional array array_sum

I would use array_map to reduce the array to only what is needed. Bear in mind, this will only work with PHP 5.3 onwards.

$total_vat = array_sum( array_map(
                 function($element){
                     return $element['vatAmount'];
                 }, 
             $account_invoices));

Just a way to do it:

$sum = 0;

foreach($account_invoices as $num => $values) {
    $sum += $values[ 'vatAmount' ];
}

If you have PHP 5.5+ you can do this without looping or using a callback (since function calls are relatively expensive) ... just use:

$sum = array_sum(array_column($account_invoices, 'vatAmount'));