If your site is running 24x7 you should not use a on demand instance, on demand instances are for temporary jobs that you need a machine for (like load balancing for extra traffic).
What you want is a heavy utilization reserved instance. You pre-pay a one time upfront fee to get a discounted hourly rate on the instance over the lifespan on the contract.
Here is a screenshot from the Simple Monthly calculator
You can see, by paying a upfront cost of $100 for a 3 year contract you get to pay $0.005 per hour for the machine instead of the $0.020 per hour for the on demand. You can see over 3 years you pay a total of $231.76 vs $527.04
Compare that to a machine that you only use 4 hours per month and you will see On-Demand is your cheapest option.
I reccomend going to the simple monthly calculator site, playing around with the settings and putting in your requirements and it should help you figure out what you will need to buy.