I’m one of the moderators of the Personal Finance sub-reddit  (at Reddit.com), which routinely sees plenty of credit score related questions. This recent one  made my blood boil when user wooga told me that his lender advised him to carry a balance to improve his score.
wooga: I was told by the lender that if I paid down to 1/3 of my balance that it would improve my score by 100 points in a few months, more then it would to keep a zero balance(or pay off each month) which is what I normally do. I didn’t believe it. …
I’m glad he didn’t because it’s flat out wrong.
Lenders would like you to believe that your credit score improves when you pay interest but it’s simply not true. Credit cards report your balance when your statement closes. They report it again when the next statement closes. They are snapshots in time with no information about what happens between those two moments. The reports are the same whether you carry a balance or pay off the balance in full, so carrying a balance does not improve your score.
It’s important to remember that the FICO credit score  is designed to calculate the likelihood you will default on a loan. Whether or not you carry a balance is not any better an indicator than your balance at statement’s close. If you charge $500, pay off $500, and then charge $500, you are no riskier than someone who charges $500, pays the minimum plus interest, and carries the $500 forward.
Don’t carry a balance if you can avoid it and certainly don’t do it because you think it’ll improve your credit score.