通过单选按钮隐藏/显示div

我试图根据一些单选按钮的值隐藏或显示一个div,css默认div为display='none'

这是输入

<input type="radio" id="payment_type" value="cash" checked="checked" name="payment_type" onchange="showhideFinancing(this.value);"/>&nbsp;Cash/Debit
<input type="radio" id="payment_type" value="cheque" name="payment_type" onchange="showhideFinancing(this.value);"/>&nbsp;Cheque
<input type="radio" id="payment_type" value="visa" checked="checked" name="payment_type" onchange="showhideFinancing(this.value);"/>&nbsp;VISA
<input type="radio" id="payment_type" value="mc" name="payment_type" onchange="showhideFinancing(this.value);"/>&nbsp;Mastercard
<input type="radio" id="payment_type" value="financing" name="payment_type" onchange="showhideFinancing(this.value);"/>&nbsp;Financing

这是部门:

<div id="financing">
...
</div>

我的Javascript fn如下所示:

function showhideFinancing(payment_type) {
    if (payment_type == "financing") {
        document.getElementById("financing").style.display = 'block';
    } else {
        document.getElementById("financing").style.display = 'none';
    }
}