How to Calculate Compound Interest — Formula & Worked Examples
What is compound interest?
Compound interest is interest earned on both your original deposit and on every bit of interest already added. Simple interest only ever grows on the original principal; compounding makes the balance grow faster every period — this is what people mean by "interest on interest".
The compound interest formula
Compound interest = A − P
Where:
- A = final amount
- P = principal (starting amount)
- r = annual interest rate as a decimal (8% = 0.08)
- n = compounding periods per year (1 = yearly, 12 = monthly, 365 = daily)
- t = time in years
Worked example — yearly compounding
$10,000 at 8% per year for 10 years, compounded annually
A = 10,000 × (1 + 0.08/1)(1 × 10) = 10,000 × 1.0810 = 10,000 × 2.1589 = $21,589
Interest earned = 21,589 − 10,000 = $11,589. For comparison, simple interest would earn only 10,000 × 0.08 × 10 = $8,000 — compounding adds $3,589 extra.
Worked example — monthly compounding
Same $10,000 at 8% for 10 years, compounded monthly:
A = 10,000 × (1 + 0.08/12)(12 × 10) = 10,000 × (1.006667)120 ≈ $22,196
Monthly compounding earns about $607 more than annual compounding on the same money.
How compounding frequency changes the result
| Frequency | n | Balance after 10 yrs |
|---|---|---|
| Annually | 1 | $21,589 |
| Quarterly | 4 | $22,080 |
| Monthly | 12 | $22,196 |
| Daily | 365 | $22,255 |
More frequent compounding always earns more, but the gains flatten out — daily adds little over monthly.
The Rule of 72 (quick mental math)
To estimate how fast money doubles, divide 72 by the annual rate:
- At 6% → 72 ÷ 6 = ~12 years to double
- At 8% → 72 ÷ 8 = ~9 years
- At 12% → 72 ÷ 12 = ~6 years
The Rule of 72, tested against the exact math
The rule says doubling time ≈ 72 ÷ rate. At 8% that predicts 9 years; the exact answer from the formula is ln(2) ÷ ln(1.08) = 9.006 years — off by about 2 days. That accuracy holds across the rates people actually meet:
| Rate | Rule of 72 | Exact years |
|---|---|---|
| 4% | 18.0 | 17.67 |
| 6% | 12.0 | 11.90 |
| 8% | 9.0 | 9.01 |
| 12% | 6.0 | 6.12 |
| 18% | 4.0 | 4.19 |
The rule drifts high below ~8% and low above it (72 ÷ 3 = 24 vs the exact 23.4; credit-card debt at 36% doubles in 2.34 years, not 2). For 2–15% it is reliably within a few months — good enough for negotiation table arithmetic, which is its real job.
The same doubling logic runs in reverse and that is its sharpest use: inflation is compounding too. At 6% inflation, prices double in ~12 years, halving your money's purchasing power in the same time. A savings account paying 4% while inflation runs 6% is a guaranteed-loss machine wearing a positive number — the inflation guide works through that arithmetic.
Monthly contributions: the formula most calculators actually use
Real saving is rarely one lump. Recurring deposits follow the future-value-of-a-series formula, FV = PMT × ((1 + i)n − 1) ÷ i, added on top of the lump-sum term. Worked example: the $10,000 lump at 8% monthly plus $200 every month for 10 years:
Lump: 10,000 × (1 + 0.08/12)120 ≈ $22,196
Contributions: 200 × ((1.006667)120 − 1) ÷ 0.006667 ≈ $36,589
Total ≈ $58,786 — of which $34,000 is what you paid in and $24,786 is interest.
Notice the structure: contributions ($200/month = $24,000 over 10 years) earned $12,589 of interest — roughly half again what the lump sum earned, because every early deposit gets its own full compounding runway. This is why the timing of contributions matters more than their size: the same $200/month started 5 years earlier is worth far more than a doubled contribution started late.
Try it instantly
Run your own numbers with the Compound Interest Calculator. Related tools:
Worked example: Compound Interest Calculator at its default inputs
Take the default setup on Compound Interest Calculator: no fields changed, nothing tuned to a nice round number. Run in the site's own engine, those values produce the answer below.
| Input | Default |
|---|---|
| Principal Amount | 10000 |
| Annual Rate (%) | 7 |
| Time (years) | 10 |
| Target Amount (for solve modes) | 20000 |
| Regular Contribution (per period) | 0 |
Result: Final Amount: $20,096.61
The steps behind that answer
- Solving for Final Amount
- Step 1: A = P(1 + r/n)^(n·t), n = 12
- Step 2: Growth of principal = $20096.61
- Step 3: No regular contributions
Principal Amount: half, as given, and half again
Hold every other field still and move only principal amount.
| Principal Amount | Result |
|---|---|
| 5,000 | Final Amount: $10,048.31 |
| 10,000 | Final Amount: $20,096.61 |
| 15,000 | Final Amount: $30,144.92 |
The middle row is the default. The outer two show how far the answer drifts when principal amount is wrong by half or by a half in the other direction.
Related guides
Frequency changes the effective rate
A nominal 6% compounded monthly is not 6% a year: (1 + 0.06/12)^12 − 1 gives 6.17%. Daily compounding gives 6.18%, and continuous compounding tops out at e^0.06 − 1, or 6.18% as well — the gains shrink quickly after monthly.
That is why regulators require an annual equivalent figure. Compare products on the effective annual rate, otherwise a monthly-compounded headline beats a quarterly one on presentation alone.
The rule of 72 is a sanity check
Dividing 72 by the annual return gives the years to double: 8% doubles in about nine years. It is accurate to within a few percent for returns between roughly 4% and 12%, and it fails badly outside that band.
Use it to check a calculator rather than replace one. If a tool says a 6% investment doubles in eight years, either the rate or the compounding assumption is wrong.
Nominal growth is not purchasing power
A 7% return with 3% inflation grows real wealth at about 3.9% a year, not 4% — the exact figure is (1.07 ÷ 1.03) − 1. Over thirty years that small difference is worth several percent of the final balance.
Model inflation explicitly when the goal is a future purchase. A retirement number computed in today money and a number computed in future money can differ by more than the contribution itself.
Frequently asked questions
Can I use this page for "yearly interest calculator"?
Yes — this guide answers the "yearly interest calculator" question: the method is explained in the sections below and the linked calculator returns the number instantly.
What is the compound interest formula?
A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal, r is the annual rate as a decimal, n is compounding periods per year, and t is years. Interest earned is A − P.
What is the difference between simple and compound interest?
Simple interest grows only on the original principal. Compound interest grows on the principal plus previously earned interest, so the balance accelerates over time.
What is the Rule of 72?
Divide 72 by the annual rate to estimate the years needed to double your money. At 8%, that is about 9 years.
Does more frequent compounding earn more?
Yes, with diminishing returns: $10,000 at 8% for 10 years reaches about $21,589 annually, $22,196 monthly, and $22,255 daily.
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