Compound interest is the reason a small savings habit can turn into a large balance, and the reason credit card debt grows so fast. It’s the same math in both cases. Here it is without the jargon.
The short version
- With compound interest, you earn interest on your interest, so growth speeds up over time.
- $10,000 at 7% a year, compounded monthly, becomes about $20,097 in 10 years.
- Rule of 72: divide 72 by the yearly rate to estimate how many years money takes to double.
- Time and the rate matter far more than how often interest compounds.
Simple vs. compound interest
With simple interest, you earn interest only on the money you put in. $10,000 at 7% simple interest earns $700 every year, forever: $17,000 after 10 years.
With compound interest, each year’s interest is added to the balance, and next year’s interest is calculated on the bigger amount. The same $10,000 at 7%, compounded yearly, is $10,700 after one year, $11,449 after two, and about $19,672 after 10, nearly $2,700 more than simple interest.
The formula
A = P × (1 + r ÷ n)n × t, where P is the starting amount, r is the yearly rate as a decimal, n is how many times a year interest is added, and t is the number of years.
Example
$10,000 at 7% compounded monthly for 10 years: 10,000 × (1 + 0.07 ÷ 12)120 ≈ $20,097. The interest earned is about $10,097, more than the original deposit.
The rule of 72
Divide 72 by the yearly interest rate to estimate how many years it takes money to double.
| Yearly rate | Rule of 72 estimate | Exact (compounded yearly) |
|---|---|---|
| 3% | 24 years | 23.4 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
It works the other way too. A credit card charging 24% doubles an unpaid balance in about three years.
Time beats almost everything
Because growth compounds, the last years add the most. $200 a month at 7% grows to about $104,185 after 20 years, but about $243,994 after 30. The extra 10 years add $24,000 of deposits but almost $140,000 to the balance, so about $116,000 of it is growth. That is why starting early, even with small amounts, matters so much.
Does compounding frequency matter?
| $10,000 at 7% for 10 years | Ending balance |
|---|---|
| Compounded daily | $20,136 |
| Compounded monthly | $20,097 |
| Compounded quarterly | $20,016 |
| Compounded yearly | $19,672 |
More frequent compounding helps a little. When you compare savings accounts, look at the APY (annual percentage yield), which already includes compounding, so accounts can be compared directly.
Where you’ll see it
- Working for you: high-yield savings, CDs, retirement accounts and long-term investments. Savings accounts and CDs at FDIC-insured banks are protected up to the insurance limits; investments are not guaranteed.
- Working against you: credit cards, unpaid loans and any debt with interest added to the balance.
Try your own numbers in our compound interest calculator, and see a table of monthly savings in how much $100 a month grows to.
Starting early vs. starting late
Example
Ava saves $200 a month from age 25 to 35, then stops, and leaves the money invested. Ben starts at 35 and saves $200 a month until 65. At an illustrative 7% a year, Ava contributes $24,000 and Ben $72,000. By 65, Ava’s balance is about $281,000 and Ben’s about $244,000. Ten early years beat thirty later ones, because Ava’s money had longer to compound.
The example uses a constant rate to show the effect; real returns vary year to year and are not guaranteed. The lesson holds anyway: time is the most powerful ingredient.
APR vs. APY
APR is a yearly rate without compounding; APY includes it. A savings account that pays 4% APR compounded monthly has an APY of about 4.07%. Banks generally advertise savings accounts by APY and loans by APR, so compare like with like.
Compound interest on debt
A $3,000 credit card balance at 24% APR, if no payments were made, would grow to about $3,804 in one year with monthly compounding. In practice you make payments, but the same math is why paying more than the minimum saves so much. Our debt payoff calculator shows how long a balance takes to clear.
