PERSONAL FINANCE / PRACTICAL GUIDE
Compound Interest Explained With a Simple Example
Compounding happens when growth is calculated on the original amount and on the growth already added to it. A higher rate and more time both increase the effect — but real investment returns vary year to year and can be negative, so a smooth compounding example is a teaching tool, not a forecast.
In this guide
- What compounding actually does
- A worked example, year by year
- Compounding versus simple interest, over longer stretches
- Now subtract a fee, and run the same math again
- Contributions can matter as much as the rate
- Use a calculator to test assumptions, not to get an answer
- Common mistakes
- What this example leaves out
- What to do next
- Sources and further reading
What compounding actually does
Simple interest pays a return on the original amount only, every period. Compounding pays a return on the original amount plus every prior period's growth, so the base it is calculated on gets larger each time. The gap between the two starts small and grows with time — which is exactly why compounding is often introduced with a chart that looks flat at first and steep later.
The same mechanism works in reverse for debt that carries interest — a balance left unpaid grows on the same math, in the wrong direction.
A worked example, year by year
Start with $1,000 at a hypothetical 5% annual return, compounded once a year, with nothing added or withdrawn. Each year's growth is 5% of that year's starting balance, not 5% of the original $1,000.
| Year | Balance at start | Growth at 5% | Balance at end |
|---|---|---|---|
| 1 | $1,000.00 | $50.00 | $1,050.00 |
| 2 | $1,050.00 | $52.50 | $1,102.50 |
| 3 | $1,102.50 | $55.13 | $1,157.63 |
| 4 | $1,157.63 | $57.88 | $1,215.51 |
| 5 | $1,215.51 | $60.78 | $1,276.28 |
By year five, that year's growth of $60.78 is larger than year one's $50.00, even though the rate never changed. The only thing that changed is the base the rate was applied to.
Compounding versus simple interest, over longer stretches
Carry the same $1,000 at 5% out to 10 and 20 years, and compare it with simple interest — 5% of the original $1,000 paid flat, every year, with no compounding.
| Years | Compounded at 5% | Simple interest at 5% | Difference |
|---|---|---|---|
| 10 | $1,628.89 | $1,500.00 | $128.89 |
| 20 | $2,653.30 | $2,000.00 | $653.30 |
Now subtract a fee, and run the same math again
Fees compound too — in the wrong direction. Take the same $1,000 at a 5% return, but with a 1 percentage point annual fee, leaving a net 4%. Rerun the 10 and 20-year figures.
| Years | At net 5% (no fee) | At net 4% (1pt fee) | Difference |
|---|---|---|---|
| 10 | $1,628.89 | $1,480.24 | $148.65 less, about 9% |
| 20 | $2,653.30 | $2,191.12 | $462.18 less, about 17% |
A single percentage point sounds small next to a 5% return. Over 20 years of compounding, it removes more than four hundred dollars from a thousand-dollar starting balance, and that gap only widens with a larger account or a longer horizon. This is the same reason a fee schedule is worth reading as carefully as a return assumption — the number attached to a fund or account is not decoration, it compounds exactly like everything else in the table.
Contributions can matter as much as the rate
Most real accounts are not one lump sum left untouched — they get regular contributions. Take $1,200 added at the end of each year, earning the same 5%, with no starting balance at all.
After 10 years, the account holds about $15,093. Of that, $12,000 was contributed directly, and the remaining $3,093 came from growth, including growth on earlier growth. Separating those two numbers matters: a plan that is behind because contributions paused tells a different story than one behind because the assumed return didn't show up.
Use a calculator to test assumptions, not to get an answer
A compounding calculator is a scenario tool. Run it once at an optimistic rate, once at a lower rate, once with a gap year where nothing was added, and once with a fee included. The spread between those runs is closer to the truth than any single number — a calculator output is a projection built on stated assumptions, not a guarantee of what an account will actually hold.
Common mistakes
- Compounding a rate that only held for one year: A strong single year does not mean that rate repeats. Investment returns vary, and some years are negative.
- Ignoring fees in the illustration: A fee that looks tiny as a percentage is not tiny once it compounds for a decade or two, as the table above shows.
- Mixing contributions into the return: Money you added is not growth. Counting it as growth overstates how well the account actually performed.
- Treating the projection as the plan: A calculator shows what happens under its assumptions. It does not adjust itself when a real year disappoints.
What this example leaves out
The illustration above uses a fixed, hypothetical rate applied once a year, with taxes ignored. Real accounts face rates that change annually, taxes that can apply to growth or withdrawals depending on the account type, and returns that can be negative in a given year, not just smaller than hoped. Even a portfolio that averages 5% over 20 years rarely does it smoothly — a real sequence might include a down year, several flat years and a strong year, in no particular order. None of that erases the underlying mechanism, growth calculated on prior growth, but it means any single projected number should be read as one scenario among several, not a promise.
What to do next
- Run your own numbers at three different rates — optimistic, moderate and low — instead of trusting one projection.
- Add your actual fee percentage to the calculator and compare the 10 and 20-year totals with and without it.
- Separate what you contributed from what came from growth in your own account, at least once a year.
Sources and further reading
New research into practice: Active vs Passive Investing: Did Your Fund Beat the Benchmark?.
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Educational purpose: This guide provides general education. It does not provide personalised financial, investment, legal or tax advice.