How compound interest works
With simple interest you earn only on the money you put in. With compound interest, the interest is added to your balance, and from then on it earns interest too. Each period, the base you earn on gets a little bigger, so growth speeds up the longer you leave the money alone.
P = starting amount · r = yearly rate (decimal) · n = compounding periods per year · t = years
Continuous compounding: A = P × e^(r × t)
Worked example
You put $10,000 into an account paying 5% a year, compounded monthly, for 10 years.
- r/n = 0.05 ÷ 12 = 0.0041667 and n × t = 12 × 10 = 120
- A = 10,000 × 1.0041667^120 = $16,470.09
Now add $100 at the end of every month. Those 120 deposits grow to $15,528.23 on their own, so the total is $31,998.32. You deposited $22,000 in all, and $9,998.32 is interest. With 3% inflation, that balance would buy about what $23,810 buys today, which is why the inflation option is worth a look.
Simple vs compound interest
Simple interest pays the same amount every year: 5% of $10,000 is $500, so after 10 years you would have $15,000. Compounding monthly turns the same rate into $16,470.09, an extra $1,470.09 that comes purely from interest earning interest. Stretch the time to 30 years and the gap becomes dramatic: simple interest gives $25,000, while monthly compounding gives about $44,677. The longer the time, the more the curve bends upward, which you can see in the chart above as the interest part of each bar grows faster than the deposits.
How often interest compounds
More frequent compounding helps, but only slightly. Here is $10,000 at 6% for 10 years:
| Compounding | Effective annual rate | After 10 years |
|---|---|---|
| Annually | 6.000% | $17,908.48 |
| Semiannually | 6.090% | $18,061.11 |
| Quarterly | 6.136% | $18,140.18 |
| Monthly | 6.168% | $18,193.97 |
| Daily | 6.183% | $18,220.29 |
| Continuously | 6.184% | $18,221.19 |
The effective annual rate, (1 + r/n)^n − 1, turns any rate into its true yearly growth. US banks show it as the APY. When you compare savings accounts or deposits, compare effective rates, not the headline rate.
The rule of 72
To estimate how long money takes to double, divide 72 by the yearly rate. The shortcut is close for everyday rates:
| Rate | Rule of 72 | Exact (yearly compounding) |
|---|---|---|
| 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: at 3% inflation, prices double in about 24 years. The calculator shows both the estimate and the exact doubling time for your rate.
Regular deposits: timing matters a little
Deposits at the start of each period earn one extra period of interest. $5,000 plus $100 a month at 6% compounded monthly for 10 years grows to $25,566.86 with start-of-month deposits and $25,484.92 with end-of-month deposits. If your deposit frequency differs from the compounding frequency (say monthly deposits into an account that compounds yearly), the calculator applies the equivalent monthly rate, so each deposit earns interest from the day it arrives. Some banks pay nothing on money until the next compounding date, so treat small differences as rounding.
Tips for using the results
- Start early. Time does most of the work. The same deposits left for 30 years instead of 20 can end up far larger, because the last decade earns interest on everything before it.
- Use a realistic rate. Savings accounts and deposits pay a known rate; investments do not. For mutual fund plans, the SIP calculator uses the conventions fund investors expect.
- Remember tax and fees. Interest may be taxed each year, which slows compounding. Fees work like negative interest.
- Compounding works against you on debt. Card and loan interest compounds too. See the real cost of borrowing with the loan calculator, and quick percentage questions with the percentage calculator.
- Want the maths in more depth? Compound interest explained covers the formula and inflation, and the rule of 72 shows how close the shortcut gets to the exact doubling time.
These results assume a constant rate and no withdrawals. They are estimates for planning, not a promise of returns.