Compound interest is interest earned on both your original principal and the interest already added to it, so your balance grows faster the longer you leave it. It is why a steady investment can multiply many times over decades, and why small differences in time or rate produce large differences in the final amount.
Simple interest pays only on the principal. Compound interest pays on the growing balance, so each period earns a little more than the last.
The formula
The future value of a compounded amount is:
A = P x (1 + r / n) ^ (n x t)
where P is the starting principal, r is the annual rate as a decimal, n is the number of times interest compounds per year, and t is the number of years. The shape of the formula explains everything below: time (t) sits in the exponent, which is why it matters most.
Growth over time
Here is how a starting amount of 10,000 grows at an 8 percent annual return, compounded yearly:
| Years | Balance | Growth |
|---|---|---|
| 1 | 10,800 | +8% |
| 5 | 14,693 | +47% |
| 10 | 21,589 | +116% |
| 20 | 46,610 | +366% |
| 30 | 100,627 | +906% |
The jump from year 20 to year 30 adds more than the entire first 20 years combined. That is compounding: the curve steepens as the balance grows.
Why starting early wins
Because time is in the exponent, the years you add at the start are worth far more than the ones you add at the end. An investor who starts ten years earlier does not get ten years of simple growth; they get ten years on the largest, fastest-growing part of the curve. For most realistic numbers, starting early beats investing more later.
Does compounding frequency matter?
A little. The same 10,000 at 8 percent over 10 years lands at:
| Compounding | Balance after 10 years |
|---|---|
| Annually | 21,589 |
| Monthly | 22,196 |
| Daily | 22,254 |
More frequent compounding helps, but the effect is small next to the rate and the time. Do not chase daily compounding; focus on a good rate and a long horizon.
Try it with your own numbers
Plug your principal, rate, and time into our compound interest calculator to see the full growth curve and the interest-versus-principal split. To model regular monthly contributions instead of a single deposit, use the SIP calculator, and to work backward from a target, the savings goal calculator.
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