JSFiddle - React, Tailwind, and code Playground

HTML

<div id="paymentchoice">Creditcard
    <input type="radio" name="payment_method" value="creditcard">Paypal
    <input type="radio" name="payment_method" value="paypal" checked>
</div>
<div id="card" class="hidden">
    <input type="text" name="cardname">
    <input type="text" name="cardnum">
    <input type="text" name="cardcode">
    <select name="month">
        <option value="01">01</option>
        <option value="02">02</option>
        <option value="03">03</option>
        <option value="04">04</option>
    </select>
    <select name="year">
        <option value="volvo">Volvo</option>
        <option value="saab">Saab</option>
        <option value="fiat">Fiat</option>
        <option value="audi">Audi</option>
    </select>
</div>
<input type="submit" value="Submit">

CSS

.hidden {
    display:none;
}

JavaScript

var options = $('#card');
var method = $('input[name=payment_method]');

method.change(function() {
    if ('creditcard' == $(this).val() ) {
        options.show();
    } else {
        options.hide();
    }
});

$('input[value=creditcard]').prop('checked', true);
options.show();