With rising interest rates, having a good credit score is crucial to keeping costs down since it can save you hundreds of dollars in monthly debt expenses.

But first, you need to understand how interest rates work. To tame inflation, the Federal Reserve has raised its effective federal funds rate from near zero in March 2022 to 5.33% as of September, per the New York Fed.

For consumers, that has resulted in rising interest rates for credit card debt, personal loans, mortgages and auto financing.

However, your credit score also determines how much money you spend on interest. The most commonly used scoring models are FICO and VantageScore, which range from a score of 300 to 850. The higher your score, the less you tend to pay in interest.

While there's not much you can do about the Fed raising interest rates, you do have some control over improving your credit score.

How much money you can save by improving your credit score

To improve your credit score, make sure you make debt payments on time and have a wide variety of credit, while using the credit you have only sparingly. It takes some work, but it can really pay off.

Depending on your outstanding debt, improving your credit score by 100 points can save you hundreds of dollars. Here's how it breaks down.

Monthly interest on a mortgage

Say your credit score is 630. You would likely qualify for an annual percentage rate of around 7.46% for a $300,000 30-year fixed mortgage, based on a Bankrate analysis from earlier this year.

However, with a credit score of 730, you would likely qualify for a lower rate, around 6.09%.

For the same $300,000 mortgage, your monthly payment would be reduced about $273 with the lower rate. Over the course of the entire loan, you'd save a total of about $98,000 in interest payments.

Monthly interest for a credit card

For credit cards, having a credit score of 630 could qualify you for an APR around 24%, according to Investopedia data. But bumping that score up 100 points to 730 would get you closer to 20%.

Now let's say you hold a $5,000 balance and interest compounds monthly. Over one month, you'd owe about $100 in interest with a 24% rate. Over a year, you'd owe about $6,340.

With the lower 20% rate, that would come out to about $83 after 30 days, and $6,097 annually.

That 4% difference saves you about $17 a month, and $240 over the course of a year.

Keep in mind that these are loose estimates, so the APR you will actually qualify for will vary with each lender. These calculations also don't take into account making minimum monthly payments on your debt.

Monthly interest on a personal loan

With a credit score of 630, you might qualify for an interest rate of around 19.9% on a personal loan, based on Bankrate estimates. But with a score of 730, that drops to something closer to 12.5%.

For a newly qualified personal loan of $5,000 spread out over 60 months, a credit score bumped up to 730 would mean a difference of $30.84 in monthly interest costs. Over the course of the loan, the difference would be $1,182 in total interest costs.

With all these numbers, it's worth noting that these calculations use interest rates that are estimates based on your credit score. The interest rates you'd actually qualify for might vary, depending on the lender.

DON'T MISS: Want to be smarter and more successful with your money, work & life? Sign up for our new newsletter!

Get CNBC's free Warren Buffett Guide to Investing, which distills the billionaire's No. 1 best piece of advice for regular investors, do's and don'ts and three key investing principles into a clear and simple guidebook.