What Is Compound Interest?
Compound interest is interest calculated on both your original money and on the interest it has already earned. Each period, your earnings are added to the balance, and the next period's interest is computed on that larger base — growth feeding growth.
The contrast with simple interest is stark over time. $10,000 at 8%:
| Years | Simple interest | Compound (annual) | Difference |
|---|---|---|---|
| 5 | $14,000 | $14,693 | +$693 |
| 15 | $22,000 | $31,722 | +$9,722 |
| 30 | $34,000 | $100,627 | +$66,627 |
In year one the difference is pocket change; by year thirty, compounding has nearly tripled the outcome. That curve — flat early, steep late — is why starting early matters more than starting big.
How to Use This Calculator
Step 1 — Initial deposit
Your starting amount. Zero is fine if you're building purely from contributions.
Step 2 — Regular contribution
What you'll add each month. This is usually the single most powerful input — steady contributions dwarf the starting balance over long horizons.
Step 3 — Annual interest rate
The yearly growth rate. For context: high-yield savings accounts have historically ranged 1–5%; diversified stock portfolios have averaged roughly 7–10% annually over long periods (with real volatility year to year).
Step 4 — Compounding frequency
How often interest is credited: annually, quarterly, monthly, or daily. More frequent compounding grows slightly faster at the same nominal rate.
Step 5 — Time horizon
Years to grow. Watch the year-by-year table below the results — the acceleration in later years is the whole lesson of compounding.
The Compound Interest Formula
For a lump sum:
- A — final amount
- P — principal (starting deposit)
- r — annual rate as a decimal
- n — compounding periods per year
- t — years
With regular contributions (an annuity), each deposit compounds from when it lands:
where PMT is the contribution per compounding period. The calculator handles the alignment between monthly deposits and your chosen compounding frequency automatically.
Worked Example: $5,000 Start + $200/Month at 7% for 20 Years
| Component | Math | Result |
|---|---|---|
| Lump-sum growth | 5,000 × (1 + 0.07/12)240 | ≈ $20,148 |
| Contribution growth | 200 × [((1.005833)240 − 1) ÷ 0.005833] | ≈ $103,935 |
| Final balance | ≈ $124,083 | |
| Total deposited | 5,000 + 200×240 | $53,000 |
| Growth earned | ≈ $71,083 |
More than 57% of the final balance is growth, not deposits — and notice the contributions out-earned the head start five to one. Consistency beats lump sums for most savers.
The Rule of 72 (and Other Useful Shortcuts)
Doubling time: divide 72 by your annual rate to estimate the years needed to double your money:
| Rate | Doubles in about | Quadruples in about |
|---|---|---|
| 3% | 24 years | 48 years |
| 6% | 12 years | 24 years |
| 9% | 8 years | 16 years |
| 12% | 6 years | 12 years |
Compounding frequency effect: at 6% nominal, $10,000 for 10 years becomes $17,908 (annual), $18,140 (monthly), $18,193 (daily). Frequency helps, but rate and time dominate — don't chase daily compounding at a worse rate.
Compound Interest Working Against You: Debt
The same math powers credit-card balances in reverse. A $5,000 card balance at 24% APR with minimum payments compounds against you the way savings compound for you — which is why balances feel immovable while paying minimums.
Two consequences worth internalizing:
- Paying off a 24% debt is a guaranteed 24% return — almost always your best available "investment."
- Order matters: attack the highest-rate balance first (avalanche method) to minimize total interest, and use our Loan Calculator to compare consolidation offers.
Six Ways to Make Compounding Work Harder
- Start now, even small. Ten early years beat twenty late ones — run the numbers above with different start dates and see.
- Automate contributions so consistency doesn't depend on willpower.
- Reinvest everything — withdrawn earnings stop compounding forever.
- Mind fees: a 1% annual fee at a 7% return forfeits about 25% of your final balance over 40 years. Prefer low-cost funds.
- Use tax-advantaged accounts (retirement accounts, ISAs, etc.) so taxes don't skim the compounding each year.
- Increase contributions with raises — even +1% of salary per year compounds dramatically. Model it with the Investment Calculator.
The Bottom Line
Compound growth is the closest thing personal finance has to magic, and it runs on just three dials: how much you feed it, what rate it earns, and how long you leave it alone. The calculator above lets you test each dial — but the year-by-year table tells the real story: the later years do the heavy lifting, and they only exist if you start.