Add an appointment booking to my site

I have a wordpress.com. I want to add an appointment booking form and a payment button. I want to sync it to my google calendar. I have a premium plan with wordpress so no plug ins. I want to use an external system which is reliable but not expensive. I have seen some for about €10 a month. If there's a free one that works, great! I am the only person using it, it's a small business start up. I'm wasting my time trawling through pages and I'm getting nowhere. I know it's a simple job but it's simple when you know how! I'm on my computer all day for correspondance and would love to get the job done asap