- Compound interest pays interest on past interest, not just on the starting amount.
- Time is the strongest lever: growth speeds up the longer money stays invested.
- A higher rate or more frequent compounding raises the final balance.
- The same math works against you on debt that is left unpaid.
What compounding means
When you save or invest money, the amount you start with is called the principal. Interest is the fee paid to you for letting someone else use that money.
With compounding, each interest payment is added to the balance. The next payment is then calculated on the new, larger balance. You earn interest on your interest.
Here is the idea with $1,000 at 5% a year:
- Year 1: $1,000 × 1.05 = $1,050.00
- Year 2: $1,050 × 1.05 = $1,102.50
- Year 3: $1,102.50 × 1.05 = $1,157.63
In year 1 you earn $50. In year 2 you earn $52.50, because the first $50 is now earning interest too. The gap looks small at first. It widens every year.
Simple interest vs compound interest
Simple interest is paid only on the principal. The interest amount is the same every period and the balance grows in a straight line.
Compound interest is paid on the principal plus all interest added so far. The balance grows along a curve that gets steeper over time.
The table shows $1,000 at 10% a year under both methods.
| Year | Simple interest | Compound interest |
|---|---|---|
| 1 | $1,100.00 | $1,100.00 |
| 2 | $1,200.00 | $1,210.00 |
| 3 | $1,300.00 | $1,331.00 |
| 4 | $1,400.00 | $1,464.10 |
| 5 | $1,500.00 | $1,610.51 |
After five years, compounding has added an extra $110.51. You can test other amounts with the simple interest calculator and the compound interest calculator.
The compound interest formula
The standard formula is:
A = P × (1 + r / n)^(n × t)
- A is the final amount.
- P is the principal, the amount you start with.
- r is the yearly interest rate as a decimal, so 5% is 0.05.
- n is how many times interest is added each year.
- t is the number of years.
For $1,000 at 10% compounded once a year for 3 years: A = 1,000 × (1.10)^3 = 1,000 × 1.331 = $1,331. That matches the table above.
The interest earned is the final amount minus the principal. Here it is $1,331 - $1,000 = $331.
How time, rate and frequency change the result
Time
Time sits in the exponent of the formula, so it has the largest effect. Money that doubles once will double again in the same number of years, and each doubling is bigger in dollars than the last. A quick shortcut is the Rule of 72: divide 72 by the yearly rate to estimate the years needed to double. At 6%, that is about 12 years. The Rule of 72 guide explains why it works.
Rate
A higher rate lifts every year of growth, and the lift itself compounds. Small differences in rate become large differences in balance over decades.
Frequency
Interest can be added yearly, quarterly, monthly or daily. More frequent compounding gives a slightly higher result. Here is $1,000 at a 12% yearly rate for one year:
| Compounding | Balance after 1 year |
|---|---|
| Yearly | $1,120.00 |
| Twice a year | $1,123.60 |
| Quarterly | $1,125.51 |
| Monthly | $1,126.83 |
Frequency helps, but much less than time or rate. The rate you actually earn after compounding is called the annual percentage yield. See APR vs APY for more on that.
Adding regular contributions
Most people do not invest one lump sum and walk away. They add money on a schedule. Each deposit starts its own compounding clock, so early deposits do the most work.
Suppose you deposit $1,000 at the start of each year and earn 10% a year:
- End of year 1: $1,000 × 1.10 = $1,100
- End of year 2: ($1,100 + $1,000) × 1.10 = $2,310
- End of year 3: ($2,310 + $1,000) × 1.10 = $3,641
You put in $3,000 and earned $641 in interest. Compare that with the single $1,000 deposit, which earned $331 over the same three years. Steady deposits give compounding more money to work on.
The habit matters more than the amount. A smaller deposit made every month for many years will often end up ahead of a larger one that starts late.
When compounding works against you
Compounding does not care which side of the loan you are on. If you owe money and interest is added to the balance, you pay interest on interest.
Take a $2,000 card balance at a 24% yearly rate, which is 2% a month, with no payments made:
- Month 1: interest is $40.00, so the balance becomes $2,040.00.
- Month 2: interest is $40.80, so the balance becomes $2,080.80.
The interest charge rises each month even though nothing new was bought. Paying only a small minimum can leave most of the balance compounding for years.
The general lesson is the same in both directions. Start saving early so time works for you, and pay down high-rate debt early so time stops working against you. The credit card payoff calculator shows how different payment amounts change the total interest.
What slows compound growth
The formula assumes every dollar of interest stays in the account and keeps earning. In practice, several things can reduce the result:
- Fees: a yearly charge taken from the balance lowers the rate you actually earn, and the loss compounds too.
- Taxes: if interest or gains are taxed along the way, less is left to grow.
- Withdrawals: money taken out early loses all the growth it would have earned later.
- Inflation: rising prices reduce what the final balance can buy.
- Changing rates: many accounts and investments do not pay the same rate every year.
None of this changes how compounding works. It simply means the rate that matters is the one you keep after costs. A projection is an estimate, not a promise, so it is worth testing a lower rate as well as the one you expect.
Try it with your own numbers
- Compound Interest CalculatorGrowth from interest earned on interest.
- Simple Interest CalculatorInterest on the original amount only.
- Future Value CalculatorWhat money today is worth later.
- Rule of 72 CalculatorHow long money takes to double.
Frequently asked questions
What is compound interest in simple terms?
Compound interest is interest paid on your starting money plus any interest already earned. Each time interest is added, the balance gets bigger, and the next interest payment is based on that bigger balance. Over many years this creates growth that speeds up, instead of the steady straight-line growth you get with simple interest.
How often is interest compounded?
It depends on the account or loan. Common schedules are daily, monthly, quarterly and yearly. More frequent compounding produces a slightly higher balance at the same stated rate. The difference between monthly and daily compounding is usually small, while the difference between a short and a long time period is large.
Is compound interest good or bad?
It is neither by itself. It helps you when you are the saver or investor, because your balance grows on top of past growth. It hurts you when you are the borrower and unpaid interest is added to what you owe. The same formula describes both cases, so the direction of the money decides the outcome.
What matters more, the rate or the time?
Both matter, but time is often the stronger factor because it is the exponent in the formula. A modest rate held for a long period can beat a higher rate held for a short one. Starting earlier usually does more for the final balance than trying to find a slightly better rate later.
This guide is general education, not financial advice. Rules of thumb vary by lender, industry and country.