Outgoing Email Limit on Free Account

Outgoing Email Limit on Free Account

Hi,

We're using Zoho Campaigns and Zoho Surveys for a short term bulk email survey.  I currently have the domain I want to use hosted with Office365 but DKIM is not working.  It may just be that the DNS has yet to propagate, but if it doesn't work soon I want to explore using Zoho Email Hosting as an alternative. 

My question is this:

Is there a limit to outgoing emails with a free hosting account?  I know IMAP and POP3 are not available with a free account which is fine since we only need to check the mail occasionally so the webmail would work fine.  We only need to send email from Zoho Campaigns, about 16,500 of them for which we are doing pay as you go.  Can we use a free email hosting account for our domain and be able to send the emails or is there some sort of limit on SMTP?  

Thanks