The days are long gone where you can charge a client by the hour. There are a very few exceptions, but even the big effects houses working on mega-budget feature films are told things like "I know that 20 years ago we gave you 90 days to animate the house being blown across the road by the tornado and we would pay for as many technicians that you have to hire to create that 10 second shot, but we need you to turn out the 1200 frames on this storyboard by next Wednesday, if you are late there will be a five grand a day penalty, and the budget is locked in at $10,000 so I'm sorry if you need to hire 40 people to do the job, the budget is fixed, take it or leave it." You never really could, and you now will never be successful if you don't ask a client what their budget is.
That's the sad reality of the VFX business. Freelance technicians have a very hard time making a living. Every one of them will go broke if they do not learn how to run a business. Running a good business is a lot more important than any design or animation skill you will ever develop.
To figure out what you need to charge you have to make an accurate assessment of your cost of doing business. You must take into account the equipment and software you have to maintain, and bookkeeping, and legal, and marketing, and even educational expenses. If you live in a major metropolitan area in the US and you are very busy, you will be lucky to have 1,000 billable hours in a 2080 hour work year. If you need to net $70,000 a year to pay your taxes, pay the rent, pay for a car, buy food, and save a little for emergencies then you have got to clear $70/hour to do that. The typical cost of doing business for a VFX technician has to be added to that. If you are working alone out of your home you are probably going to have to add at least another $15 or $20 an hour to that.
But wait, I said that you can't really charge by the hour, so how does that make any sense? What I am calling Billable Hours are the actual hours that you work on a project. That does not include any of the other things you do every day. If you are really well organized and you are basically working alone, you will be lucky to spend half of your workday actually doing something for a client. So how do you figure out what to charge for a job. You figure out how many hours you actually expect to work on the project, then multiply that by about $85, and that is what is going to cost to do the job and make a profit, and it is all about making a profit. If you do not make a profit you will go broke and end up waiting tables.
You said you expect to spend 3 to 4 days working on the project, so round that to about 30 hours. You would need to charge $2550 for the project. I don't know any client that would be willing to pay that much for 12 seconds of the kine of animation you are describing and some kind of number counter.
You should have never taken the job without finding out what their budget expectations are for something that simple. If their budget is $500, then you need to get to a place where you can do that job in a couple of hours, spend another couple of hours interacting with the client, and an hour writing the contract, sending the invoice, and doing the books. I don't care if you are a beginner. The client doesn't care. Their only concern is the end product. You have to care about how long it takes you to do the job. You also have to be honest with yourself when you calculate your cost of doing business.
How do I know this stuff. I started working full time in television on September 3, 1969 - nearly 50 years ago. Less than a year later I was working on my first feature film. I got my first business license in 1972, started buying gear and freelancing, and I'm still at it. I've gone broke twice, ran a company for several years with as many as 13 employees, had a client list that included some of the biggest companies in the world and some of the most prestigious advertising agencies, gone 3 years without a single profitable job, and somehow still managed to raise a family and take an occasional vacation. I've put in 90 hour weeks, and I have also been paid a ridiculous amount for a few hours work solving a problem for a client. The very hardest thing I had to learn in all those years was how to treat my career as a business. I still struggle with that at least once a month when I'm tempted to spend an extra 20 hours on a project that should have only taken 4.
Sorry for the rant... Call the client, find out what their budget is, then work as fast as you can to deliver the project in enough time to make a profit.
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