How exactly does paying your credit card balance in full increase your credit score?

Your credit score increases when you consistently pay on time.

As the months and years go by, the length of the credit history goes up which helps that sector of your score. The lack of negative reports in your history helps your payment history sector of your score.

According to myFICO:

Payment history (35%)

The first thing any lender wants to know is whether you've paid past credit accounts on time. This helps a lender figure out the amount of risk it will take on when extending credit. This is the most important factor in a FICO Score.

Be sure to keep your accounts in good standing to build a healthy history.

Length of credit history (15%)

In general, a longer credit history will increase your FICO Scores. However, even people who haven't been using credit for long may have high FICO Scores, depending on how the rest of their credit report looks.

You mention that you will by paying off part of the balance before the statement closes, and wonder what number is reported. The number is reported one time a month. You actually hope that based on the numbers you used in your example that they don't report the higher numbers you cite. That is because credit utilization is part of the score. And in this case a high utilization of revolving credit is bad. Lenders don't like customers that are flirting with their credit limits.

Again according to myFICO

Amounts owed on accounts determines 30% of a FICO® Score

FICO research has found that your level of debt is predictive of future credit performance because the amount owed typically impacts your ability to pay all monthly credit obligations on time. Not to worry if you have debt — it doesn't automatically make you a high-risk borrower. However, as your balances increase so does the probability of difficulty meeting monthly payments on time, but that's just part of what determines your credit score.

One of the parts of amounts owed it credit utilization of your credit cards.

Credit utilization ratio on revolving accounts

Your credit utilization ratio on revolving accounts-the percentage of your available credit you're using-is an important factor in your FICO Scores. Using a high percentage of your available credit means you're close to maxing out your credit cards, which can have a negative impact on your FICO Scores.

On the other hand, using a low percentage of your available credit can have a positive impact. In some cases, a low credit utilization ratio will have a more positive impact on your FICO Scores than not using any of your available credit at all.

It's also important to note that your current account balance isn't necessarily the balance that shows up on your credit report. Your account balance on your credit report will reflect the account balance your lender reported to the credit bureau (typically the balance from your latest monthly statement). So even if you pay your credit card balances in full each month, your account balance won't necessarily show on your credit report as $0.

The good news about the utilization part of the score is that it isn't sticky. If the next month the reported number is low, then that portion of the score calculation won't hurt you.

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Added information about the reported balance.

Lets say you buy $100 of groceries every weekend. At the end of the first billing cycle you will have a balance of lets say $400 on the credit card, and you will have to pay that bill in 3 weeks. That will mean that by the time you pay the bill of $400, you will have bought groceries 3 more times and your balance will not be zero it will be $300. A week later when the second cycle closes the balance will be $400. The highest balance that could be reported is $700 just before you pay the bill, the lowest will be $300, but many will just report $400 because that is what you are billed.

In the situation described above you get points for using the card, and you don't lose points for being close to the limit. There is no benefit to your score to pay off the balance before they generate the bill, unless you are very close to the limit. But score wise that is only important for this cycle because that portion of score has no history.

There are other benefits to paying off the bill early if you are close to the limit, but that is due to wanting to have room in case of an emergency.