What Is Compound Interest, Really?
Compound interest gets described as magic, or as the “eighth wonder of the world.” Stripped of the drama, it’s a straightforward idea - and once you see it, you understand why starting early matters so much.
Interest on your interest
Simple interest is earned only on the amount you originally put in. Compound interest is earned on your original amount plus all the interest you’ve already earned. Each period, the interest itself starts earning interest.
Imagine you save a sum and it earns interest in year one. In year two, you earn interest not just on your original savings but also on that first year’s interest. The base you’re earning on keeps growing, so each year adds a little more than the last. Early on the difference looks tiny. Over many years it becomes dramatic.
Why time is the real ingredient
The single biggest factor in compounding isn’t how much you put in - it’s how long it has to grow. Money left to compound for thirty years pulls far ahead of the same amount left for ten, because it goes through many more cycles of earning-on-earnings.
This is why the common advice is to start saving or investing early, even with small amounts. A modest sum with decades to grow can outrun a larger sum that started late. Time is doing most of the work.
Where the rule gets misapplied
- Assuming growth is roughly linear, like simple interest. Compound growth accelerates over time, so eyeballing “double the years, double the money” understates what actually happens.
- Waiting to start “until there’s more to invest.” Since time does most of the work in compounding, waiting even a few years to begin can cost more than adding a larger sum later would make up for.
- Only thinking of compounding as something that helps you. On debt, the identical mechanism works in reverse. Unpaid interest gets added to the balance and then charged interest itself, which is why carrying high-interest debt can be more costly than it first appears.
- Not checking how often interest compounds. Compounding annually, monthly, and daily on the same stated rate produce different results. More frequent compounding grows a balance faster, and a debt faster too.
- Making only minimum payments on high-interest debt without accounting for compounding. Small required payments can leave a balance shrinking very slowly, or not at all, while interest keeps compounding on what’s left.
The same force, running backwards
Compounding isn’t only your friend. On debt - especially high-interest debt like credit cards - interest compounds against you. Unpaid interest gets added to your balance, and then you’re charged interest on that larger balance too. This is exactly how a balance can balloon when only minimum payments are made.
Worth remembering
Compound interest rewards patience and punishes delay. On savings, the earlier you start and the longer you leave it, the more the growth accelerates. On debt, that same acceleration is why paying down high-interest balances quickly matters so much. Same mechanism, two very different directions.
The full 30-year calculation
Inputs below are illustrative and chosen to show the mechanics. Rates and limits change, so check the current figure at the source cited under Sources before relying on any of these numbers.
| Year | You contributed | Growth | Balance | Growth as % of balance |
|---|---|---|---|---|
| 1 | $2,400 | $79 | $2,479 | 3.2% |
| 2 | $4,800 | $336 | $5,136 | 6.5% |
| 3 | $7,200 | $786 | $7,986 | 9.8% |
| 4 | $9,600 | $1,442 | $11,042 | 13.1% |
| 5 | $12,000 | $2,319 | $14,319 | 16.2% |
| 6 | $14,400 | $3,432 | $17,832 | 19.2% |
| 7 | $16,800 | $4,800 | $21,600 | 22.2% |
| 8 | $19,200 | $6,440 | $25,640 | 25.1% |
| 9 | $21,600 | $8,372 | $29,972 | 27.9% |
| 10 | $24,000 | $10,617 | $34,617 | 30.7% |
| 11 | $26,400 | $13,198 | $39,598 | 33.3% |
| 12 | $28,800 | $16,139 | $44,939 | 35.9% |
| 13 | $31,200 | $19,466 | $50,666 | 38.4% |
| 14 | $33,600 | $23,207 | $56,807 | 40.9% |
| 15 | $36,000 | $27,392 | $63,392 | 43.2% |
| 16 | $38,400 | $32,054 | $70,454 | 45.5% |
| 17 | $40,800 | $37,225 | $78,025 | 47.7% |
| 18 | $43,200 | $42,944 | $86,144 | 49.9% |
| 19 | $45,600 | $49,250 | $94,850 | 51.9% |
| 20 | $48,000 | $56,185 | $104,185 | 53.9% |
| 21 | $50,400 | $63,795 | $114,195 | 55.9% |
| 22 | $52,800 | $72,129 | $124,929 | 57.7% |
| 23 | $55,200 | $81,239 | $136,439 | 59.5% |
| 24 | $57,600 | $91,180 | $148,780 | 61.3% |
| 25 | $60,000 | $102,014 | $162,014 | 63.0% |
| 26 | $62,400 | $113,805 | $176,205 | 64.6% |
| 27 | $64,800 | $126,621 | $191,421 | 66.1% |
| 28 | $67,200 | $140,538 | $207,738 | 67.7% |
| 29 | $69,600 | $155,634 | $225,234 | 69.1% |
| 30 | $72,000 | $171,994 | $243,994 | 70.5% |
Show your work: formula, assumptions, and what was checked
Formula
balance(m) = balance(m-1) * (1 + r/12) + contribution
r = 7% nominal annual, compounded monthly
contribution = $200 at the end of each month, 360 months
Assumptions used in the table above
- $200 contributed monthly, never increased
- 7.0% nominal annual return, applied monthly, no fees or taxes modelled
- Starting balance $0
Verification
Table computed by scripts/artifacts.py (function grow). The 30-year balance of $243,994.20 is reproducible by running that function with the inputs above. No figure here is taken from a third party.
The inputs above are fixed so the arithmetic can be checked. To run it on your own figures, use the compound interest calculator.