EDUCATION

How does interest actually work?

The same math that grows a savings account also grows a credit card balance. Once you can see the mechanism, both make a lot more sense. General information, not personalized financial advice.

The short version: interest is a percentage of money, charged or paid on a schedule. Simple interest is calculated only on the original amount, so it grows in a straight line, the same dollar amount every time. Compound interest is calculated on the original amount plus whatever interest has already piled up, so it curves upward: slow at first, then much faster. That curve is one of the most powerful forces in personal finance. It works exactly the same way whether it's growing your savings or growing what you owe.

Simple interest vs. compound interest

One grows in a straight line. The other curves.

Simple interest is the easy version. Every year, you earn interest on the same starting amount, nothing more. A $1,000 balance earning 6% simple interest earns exactly $60 a year, every single year, because the math is always based on that same original $1,000. Written as a formula, it's interest = principal × rate × time.

Compound interest adds a twist. Each time interest gets calculated, it's added to the balance. So the next round of interest is calculated on a slightly bigger number than before. That's really the whole idea: interest earning interest. If you want the exact formula, it's A = P(1 + r)^t, where P is the starting amount, r is the rate, and t is the number of time periods. The extra interest-on-interest doesn't look like much in year one, but it adds up, literally, into a real gap over time.

Simple interest

Compound interest

$1,000 at 6% a year, either way. Simple interest earns the same flat $60 every year, for a straight line to $2,200 after 20 years. Compound interest earns 6% of a slightly larger number each year, curving up to $3,207, over $1,000 more, without depositing another dollar. Hover or tap any point above for the exact numbers at that year.

Why the rate matters more than almost anything else

A few points of rate compounds into a very different outcome.

Compounding speeds up over time instead of growing at a steady pace. That means small differences in rate stop looking small once enough years go by. Doubling the rate doesn't just double your outcome. It does even more than that, because the extra growth is also earning its own interest.

3% return

6% return

9% return

Same $1,000, same 30 years. The only thing that changes is the rate: 3% ends at $2,427, 6% more than doubles that to $5,743, and 9% more than doubles it again to $13,268. Tripling the rate did not triple the outcome. It multiplied it by roughly five and a half.

How often it compounds

Compounding more often helps a little. The rate itself matters far more.

This is also where two similar-looking terms, APR and APY, come apart. APR (annual percentage rate) is just the stated rate, before compounding is factored in. APY (annual percentage yield) is what you actually earn or owe once compounding within the year gets added in. So APY is always a little higher than APR, whenever compounding happens more than once a year.

For the curious, here's the full formula with compounding frequency built in: A = P(1 + r/n)^nt, where n is how many times a year interest compounds. In plain terms: put $2,000 in at a 5% APR for 3 years. Compounded monthly instead of once a year, it grows to $2,322.94 instead of $2,315.25, a difference of $7.69. Compounding more often is a real effect. It's just a small one next to the rate.

$10,000 at 6% APR, held for 10 years. Compounding daily instead of annually adds about $312, roughly a third of one percent of the total. The rate did nearly all of the work; how often it compounded barely moved the needle. This is why comparing APY, not just the advertised APR, matters more when rates or terms differ than when only the compounding schedule does.

A shortcut worth memorizing

The Rule of 72: divide 72 by the rate to estimate years to double.

Working out the full formula by hand is more math than most people want to do in the middle of a conversation. The Rule of 72 is a mental-math shortcut instead: divide 72 by the rate (as a whole number, like 6, not 0.06) and you get roughly how many years it takes money to double. It's surprisingly accurate for the rates most savings accounts, investments, and loans actually use.

72 ÷ 3 = about 24 years to double

72 ÷ 6 = about 12 years to double

72 ÷ 9 = about 8 years to double

12%

72 ÷ 12 = about 6 years to double

Checked against the exact formula, this shortcut lands within a few months in the 6% to 9% range, and drifts a bit further at the extremes. Still close enough for a quick gut check on any rate you're offered, whether it's a savings account, an investment return, or an interest rate on debt.

The same math, working against you

Compounding doesn't care whether the balance is yours or a debt.

Everything above works exactly the same way on money you owe. A credit card balance compounds too, usually every month, and usually at a much higher rate than any savings account pays you. Making only the minimum payment keeps your account in good standing. A common formula for that minimum is 2% of the balance or $25, whichever is larger. But it's built to just barely cover the interest, plus a sliver of what you actually owe. Most of that payment goes toward interest that already piled up, not toward what you originally spent.

Minimum payments only

Fixed $200/month

A $5,000 balance at 22% APR. Paying only the minimum barely dents it: after 10 years you would still owe about $4,093, and at that pace it would take decades longer to finish, costing far more in interest than the original $5,000 itself. A fixed $200 a month clears the same balance in under 3 years and costs roughly $1,750 in interest instead.

This is exactly why federal law requires every credit card statement to show two numbers: how long it would take to pay off your current balance at the minimum payment, and how much interest that would cost you in total. It's one of the more genuinely useful boxes on a statement, and one of the easiest to skip over.

Putting it together

Three variables decide everything: rate, time, and how often it compounds.

The rate matters most, by far. That's why even a couple of points of difference on a savings account, an investment, or a loan is worth paying attention to. Time is the second lever, and it works quietly: money given more years to grow ends up worth more than money added later. That's the entire case for starting early. How often the interest compounds matters least of the three, a real effect, but usually a small one next to the other two.

The same math means paying down a high-rate balance fast is one of the best guaranteed uses of extra money most people have. Paying off a 22% APR balance early is, in effect, a 22% guaranteed return on your money, higher than most investments reliably offer.

Where this comes from

Compound interest and Rule of 72 figures

Calculated directly from the standard compound-interest formula, A = P(1 + r/n)^nt. This is established financial mathematics, not sourced from any single publisher.

Minimum payment disclosure requirement

Credit CARD Act of 2009 statement disclosure rules, via LoanPro's summary of CARD Act requirements.

This page explains how interest generally works; it isn't financial advice, and actual rates, compounding schedules, and payment formulas vary by account and lender. Check your own account terms for the numbers that actually apply to you.