Compound interest is interest earning interest. Over a year the difference against simple interest is negligible; over thirty years it is the difference between a modest sum and a large one. The mechanism is unremarkable — each period's gain becomes part of the base for the next — but the result is exponential, and human intuition about exponential growth is reliably poor.
The same force runs in reverse on debt. A credit card at 22% APR compounding monthly does to your balance exactly what a good investment does to your savings, which is why carrying a card balance while trying to invest rarely makes sense.
The formula
A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year, and t the number of years. With regular contributions the calculation adds a second term for the future value of the payment stream, which is what makes monthly investing so much more effective than a single deposit of the same total.
$10,000 at 7%, left alone
| Years | Balance | Interest earned |
|---|---|---|
| 5 | $14,026 | $4,026 |
| 10 | $19,672 | $9,672 |
| 20 | $38,697 | $28,697 |
| 30 | $76,123 | $66,123 |
| 40 | $149,745 | $139,745 |
The rule of 72
Divide 72 by the annual rate to get the approximate years to double. At 6%, money doubles in about twelve years; at 9%, in eight. It is accurate enough for mental arithmetic anywhere between about 4% and 12%, and it makes the cost of a lower return immediately visible — the difference between 6% and 8% is not a fifth more money, it is a doubling cycle every nine years instead of every twelve.
What the projection cannot tell you
- Inflation: a 7% nominal return with 3% inflation is roughly 4% in real purchasing power. Model in real terms if the goal is decades away.
- Sequence of returns: markets do not deliver a smooth average, and a poor first decade behaves very differently from a poor last one.
- Fees: a 1% annual charge can consume around a quarter of a forty-year outcome.
- Tax: the compounding is very different inside and outside a tax-sheltered account.
Related tools
- Percentage Calculator
- Loan Calculator — compounding working against you
- Mortgage Calculator
- Browse all free tools