Madrid is not recommended as a TEFL option.

I would strongly recommend that you don't consider TEFL in Madrid as a viable option unless work can be had with  the British Council, or perhaps International House. Contracts are part-time but 'zero hour', 'obras y servicios', which means that there's no sick pay or holidays to speak of. If you have been able to begin work in September you can't even assume that classes can be guaranteed until late December. Every month in Spain there are holidays, except February, and if these fall on a Tuesday or a Thursday that's half a week without pay! 'Summer' begins mid-June, which'll mean no work for three months, so over a year you might earn 600 euros/month.

On contract 15-16 euros an hour is the norm, and less than 24 euros an hour if freelance.

Some academias such as 'Monkey Language Services' such be avoided like the plague; they pay extremely late and have  been known to invite teachers to leave the classroom in the middle of a session whilst they 'talk' to clients.

Remember one 'madrileño' in four is on less than 900 euros a month, and with unemployment at 23%. Things have been looking bad since 2009 and the new government elected Dec. 20th will have to make cuts of 9 billion euros!