Dyamic DNS wihtin dns-stock.com is free of charge.
Dynamic DNS points a hostname to a static or dynamic IP. You can even host your webpage for free at home.
First, add an A record to the DNS zone of your domain with the hostname you want,
ex.: for athome.dns-stock.com you add an A record pointing to 126.96.36.199 with the hostname athome.
Now enter the config menu of your router and configure as follow:
Dynamic DNS provider : User-defined
Update-URL : http://dyndns.dns-stock.com/?hostname=<domain>&username=<username>&password=<pass>&myip=<ipaddr>
Domainname: yourhost.yourdomain.tld (ex.athome.dns-stock.com)
Username: the username you defined when you created the dynamic DNS entry
Password: the password you defined when you created the dynamic DNS entry
The values passed to the different querystring variables in the update-url (<domain>, <username>, <pass>, <ipaddr>) come from your router. Please read the manual of your router.