Compound interest is interest earned on your principal plus all the interest you have already accumulated. A $10,000 deposit at 6% compounded monthly becomes $18,194 after 10 years — compared to just $16,000 with simple interest. The difference ($2,194) is pure compounding at work.
What Is Compound Interest?
When you deposit money in a savings account, the bank pays you interest on your balance. With simple interest, you only earn interest on your original deposit. With compound interest, each interest payment is added to your balance and then earns interest itself.
Over long periods, this creates exponential rather than linear growth — what Albert Einstein is often credited with calling “the eighth wonder of the world.”
The Compound Interest Formula
$$A = P\left(1 + \frac{r}{n}\right)^{nt}$$
Where:
- A = final amount (principal + interest)
- P = principal (starting balance)
- r = annual interest rate (decimal form; 5% = 0.05)
- n = number of compounding periods per year
- t = time in years
Interest earned = A − P
Worked Example: $10,000 at 6% Over 10 Years
Using the formula with monthly compounding (n = 12):
$$A = 10{,}000 \times \left(1 + \frac{0.06}{12}\right)^{12 \times 10} = 10{,}000 \times (1.005)^{120}$$ $$A = 10{,}000 \times 1.8194 = $18{,}194$$
| Method | After 10 Years | Interest Earned |
|---|---|---|
| Simple interest (6%) | $16,000 | $6,000 |
| Compound — annual (6%) | $17,908 | $7,908 |
| Compound — monthly (6%) | $18,194 | $8,194 |
| Compound — daily (6%) | $18,221 | $8,221 |
The difference between simple and daily compounding is $2,221 over 10 years — without adding a single additional dollar.
How Compounding Frequency Affects Growth
Most savings accounts compound daily and credit interest monthly. The APY (Annual Percentage Yield) automatically accounts for compounding frequency, which is why APY is a more useful comparison metric than the nominal rate.
| Compounding | n per Year | $10,000 at 5% after 1 Year |
|---|---|---|
| Annually | 1 | $10,500.00 |
| Quarterly | 4 | $10,509.45 |
| Monthly | 12 | $10,511.62 |
| Daily | 365 | $10,512.67 |
The Rule of 72: Doubling Time
A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money.
| APY | Doubles In (Approx.) |
|---|---|
| 1% | 72 years |
| 2% | 36 years |
| 4% | 18 years |
| 5% | 14.4 years |
| 7% (stock market avg) | ~10.3 years |
| 10% | 7.2 years |
At the current national average savings rate of 0.46% APY, your money would take 156 years to double. At a 5.00% high-yield savings account, it doubles in roughly 14 years.
Compound Interest Working Against You: Debt
The same math that grows savings also amplifies debt. The average credit card APR in 2026 is approximately 21.5%.
If you carry a $5,000 credit card balance at 21.5% APR (compounded daily) and make only minimum payments:
- After 1 year: ~$1,075 in interest added
- After 5 years: the balance could grow to over $14,000 if only minimums are paid
Paying off high-interest debt is the guaranteed equivalent of earning that interest rate — a 21.5% return you can’t reliably beat in any investment.
Compound Interest in Savings vs. Investing
Compounding works for savings accounts, CDs, and bonds — but also for investment returns. A stock portfolio earning an average 8% annually will grow from $10,000 to:
- $21,589 after 10 years
- $46,610 after 20 years
- $100,627 after 30 years
This is why starting early matters far more than the amount contributed. Time is the multiplier that compound interest depends on.
See also: what counts as a good interest rate in 2026 and how low-APY vs. high-APY accounts compare in actual dollar terms.
For the full picture on rates, visit the Interest Rates & Federal Reserve hub.
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