Compound interest pays you interest on your interest. Over short periods the effect is unremarkable; over decades it dominates everything else about an investment, and it is the single strongest argument for starting early.
The formula
With continuous compounding the limit becomes A = Pe^(rt), the theoretical maximum for a given nominal rate.
A = P(1 + r/n)^(nt) A = final amount P = principal r = annual rate n = compounds per year t = years
Simple versus compound
$10,000 at 7% for 30 years:
| Method | Final value | Interest earned |
|---|---|---|
| Simple interest | $31,000 | $21,000 |
| Compounded annually | $76,123 | $66,123 |
| Compounded monthly | $81,165 | $71,165 |
| Compounded daily | $81,646 | $71,646 |
Compounding frequency matters far less than rate and time. Moving from annual to daily adds about 7%; adding ten years adds nearly 100%.
The rule of 72
Divide 72 by the annual percentage rate to estimate the doubling time. At 6% money doubles in roughly 12 years; at 9%, roughly 8.
The approximation is accurate within a few percent for rates between about 4% and 12%, which covers most realistic investment planning.
Years to double ≈ 72 / interest rate (%)
Why starting early beats saving more
Two savers, both earning 7%. Anna invests $5,000 a year from 25 to 35, then stops — ten contributions, $50,000 total. Ben starts at 35 and invests $5,000 a year until 65 — thirty contributions, $150,000 total.
At 65 Anna has roughly $602,000 and Ben roughly $540,000. Anna invested a third as much and still finished ahead, purely because her money compounded for an extra decade.
Inflation works the same way against you
Compounding is symmetric. At 3% inflation, purchasing power halves in about 24 years — so a nominal 7% return is closer to 4% in real terms.
When projecting decades ahead, decide explicitly whether you are working in nominal or real terms, and keep it consistent.
Worked example
Using the values pre-loaded in the calculator above:
| Input | Value |
|---|---|
| Principal ($) | 5000 |
| Annual rate (%) | 6 |
| Years (yrs) | 10 |
| Compounds per year | Monthly |
| Output | Value |
|---|---|
| Future value | $9,096.98 |
| Interest earned | $4,096.98 |
| Effective annual yield (APY) | 6.1678% |
| Growth multiple | 1.8194× |
Frequently asked questions
What is the difference between APR and APY?
APR is the nominal rate ignoring compounding. APY includes it. At 12% nominal compounded monthly, the APY is 12.68%. Savings products advertise APY; loans advertise APR.
How often should interest compound?
More often is better for savings, but the gains taper quickly. Daily versus annual compounding at 7% differs by roughly 0.25 percentage points of effective yield.
Does compound interest apply to debt?
Yes, and it works against you. Credit card interest typically compounds daily, which is why a balance carried at 22% APR grows so much faster than the headline rate suggests.
What return should I assume?
Historically, broad equity markets have returned roughly 7% annually after inflation over long periods, with substantial variation. Conservative planning uses lower figures; no past return guarantees a future one.