How compound interest works
Compound interest means your interest earns interest. Each period, the balance grows by the rate, and from then on the new (larger) balance is what earns interest next period. Over long horizons, this is how relatively small monthly contributions become large balances.
The core formula for a lump sum is:
A = P · (1 + r/n)^(n·t)
Where P is the principal, r is the annual rate, n is compounds per year, and t is years. Monthly contributions are added at the end of each month and compound from then on. When you pick a frequency other than monthly, we convert it to the equivalent monthly rate so contributions are treated fairly.
Working it out by hand
Take $10,000 at 7% compounded once a year for three years, with no extra deposits.
- Year 1: $10,000 × 1.07 = $10,700.00. You earned $700.
- Year 2: $10,700 × 1.07 = $11,449.00. You earned $749, because the first year's $700 also earned interest.
- Year 3: $11,449 × 1.07 = $12,250.43. You earned $801.43.
- Check with the formula: $10,000 × 1.07³ = $12,250.43. Total interest is $2,250.43, compared with $2,100 from simple interest.
Each year's interest is larger than the last. That gap between simple and compound interest widens every year you stay invested.
Growth over time
| Years | You put in | Final balance | Interest earned | Growth multiple |
|---|---|---|---|---|
| 5 | $22,000 | $28,495 | $6,495 | 1.30× |
| 10 | $34,000 | $54,714 | $20,714 | 1.61× |
| 20 | $58,000 | $144,573 | $86,573 | 2.49× |
| 30 | $82,000 | $325,159 | $243,159 | 3.97× |
Between years 20 and 30 you add only $24,000 more, yet the balance grows by more than $180,000. Most of the growth in a long plan arrives at the end, which is why starting early matters. Saving $200 a month at 7% for 40 years gives about $524,963; waiting ten years and saving for 30 years gives about $243,994.
Does compounding frequency matter?
| Compounding | Final balance |
|---|---|
| Annually | $16,288.95 |
| Semi-annually | $16,386.16 |
| Quarterly | $16,436.19 |
| Monthly | $16,470.09 |
| Daily | $16,486.65 |
Going from annual to daily compounding adds under $200 over ten years. Raising the rate or the number of years changes the result far more.
Assumptions
This calculator assumes a constant rate of return and monthly contributions. It ignores taxes, account fees and inflation. Real-world investment returns vary from year to year; the result is a projection, not a guarantee or financial advice.