About the Compound Interest
Compound interest is interest earned on interest already earned. It is the mechanism behind long-term wealth building and the reason starting early matters more than contributing heavily later — the growth curve is exponential rather than linear, and almost all of it arrives at the end.
The formula
A = P(1 + r/n)^(nt) + C · [((1 + r/n)^(nt) − 1) / (r/n)]P is the initial principal, r the annual rate, n the compounding periods per year, t the years, and C the regular contribution per period. The first term grows the lump sum; the second grows the contributions.
How to use this calculator
- 1Enter your Initial Investment ($). The field starts at
10000, which you can overwrite. - 2Enter your Annual Interest Rate (%). The field starts at
7, which you can overwrite. - 3Enter your Years to Grow. The field starts at
10, which you can overwrite. - 4Enter your Monthly Contribution ($). The field starts at
500, which you can overwrite. - 5Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Initial Investment ($) | 10000 |
| Annual Interest Rate (%) | 7 |
| Years to Grow | 10 |
| Monthly Contribution ($) | 500 |
Result
Total Balance: $106,639.02
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
The exponential shape is what defies intuition. Ten thousand dollars at 7 percent becomes roughly 19,700 after ten years, 38,700 after twenty, and 76,100 after thirty — each decade adds more than the entire preceding balance. This is why an investor who starts at 25 and stops at 35 can finish ahead of one who starts at 35 and contributes for thirty years.
Compounding frequency matters far less than rate and time. Moving from annual to monthly compounding at 7 percent adds about 0.23 percentage points to the effective yield; moving from 7 percent to 8 percent adds a full point, and adding ten years to the horizon roughly doubles the result. Time is the dominant variable and the only one you cannot buy back.
Things worth knowing
- The rule of 72 gives a fast estimate: divide 72 by the rate to get the doubling time. At 7 percent, money doubles roughly every ten years.
- Fees compound against you exactly as returns compound for you. A 1 percent annual fee can consume a quarter of a lifetime portfolio.
- Inflation erodes the real value of the result. A nominal 7 percent return is closer to 4 percent in purchasing power.
- Tax-advantaged accounts let compounding work undisturbed, which is worth more than most people assume over decades.
- Consistency beats timing. Regular contributions through downturns are what capture the recovery.
Frequently asked questions
What is the difference between simple and compound interest?+
Simple interest is calculated only on the original principal. Compound interest is calculated on principal plus accumulated interest, so it grows exponentially. Over thirty years the difference is enormous.
How does the rule of 72 work?+
Divide 72 by the annual return rate to estimate how many years until money doubles. At 6 percent that is 12 years, at 9 percent about 8. It is accurate enough for mental arithmetic at typical rates.
Does compounding frequency make much difference?+
Less than most people expect. At 7 percent, monthly rather than annual compounding raises the effective yield by roughly 0.23 percentage points. The rate and the time horizon matter far more.
Why does starting early matter so much?+
Because the last doublings are the largest. Money invested in your twenties has time for four or five doublings; money invested in your fifties may only manage one, so the early contributions do most of the work.