I'd be a little weary of keeping cooked rice for a week, even in a good fridge (my fridge stays at a solid 2C, which keeps most things good to eat for long than you'd think!). Rice is a surprisingly good vector for food poisoning due to it's often carrying Bacillus Cereus spores which are heat resistant and can then germinate and grow in the fridge - most of the sources I've seen suggest that you shouldn't keep cooked rice in the fridge for more than 1 to 3 days.

Anecdote - Of all the times I've had food poisoning, probably half of them have been because I've kept cooked rice around too long. I might just be unlucky though!