How Compound Interest Works
The complete guide to the compound interest formula and why consistent contributions matter more than most people realize.
What is compound interest?
Compound interest is interest earned on both your initial principal and the interest that has already accumulated. Each period, your interest is added to the principal, so the next period you earn interest on a slightly larger base. This self-reinforcing effect is why Albert Einstein reportedly called compound interest the "eighth wonder of the world."
The practical difference: $10,000 invested at 7% for 30 years grows to about $31,000 with simple interest versus over $76,000 with compound interest — that gap widens dramatically with time.
The compound interest formula
A = P × (1 + r/n)^(n×t)
- A — Final amount (principal + interest)
- P — Initial principal (your starting deposit)
- r — Annual interest rate as a decimal (7% = 0.07)
- n — Compounding periods per year (12 for monthly, 365 for daily)
- t — Time in years
For accounts with regular monthly contributions, the formula adds a future value of annuity term: PMT × [((1 + r/n)^(n×t) − 1) / (r/n)], where PMT is the recurring payment amount.
Compounding frequency
The more often interest compounds, the faster your money grows. Here's how the same $10,000 at 7% for 20 years differs by compounding frequency:
| Frequency | Periods/year | Balance after 20 years |
|---|---|---|
| Annually | 1 | $38,697 |
| Quarterly | 4 | $39,354 |
| Monthly | 12 | $39,543 |
| Daily | 365 | $40,275 |
The Rule of 72
A quick mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money.
At 7% annual return: 72 ÷ 7 ≈ 10.3 years to double.
At 10% annual return: 72 ÷ 10 ≈ 7.2 years to double.
Why monthly contributions matter
Consistent monthly contributions are often more powerful than increasing your initial deposit. Each contribution starts earning compound interest immediately. Over 30 years at 7%, an extra $500/month added to a $10,000 starting balance results in over $600,000 — most of which is interest, not your own money.
Starting 10 years earlier with the same contributions consistently outperforms starting later with a larger lump sum — time in the market is the most powerful variable.
Frequently asked questions
What is compound interest?▼
Compound interest is interest calculated on both your initial principal and the accumulated interest from previous periods. Unlike simple interest, which only earns on the principal, compound interest accelerates growth over time — often called 'earning interest on interest.'
What is the compound interest formula?▼
The standard compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the time in years. For accounts with regular contributions, the formula extends to include a future value of annuity component.
How does compounding frequency affect growth?▼
The more frequently interest compounds, the faster your balance grows. Daily compounding produces slightly more than monthly, which produces more than annual compounding. The difference is small at typical savings rates (under 1% annually) but becomes more noticeable at higher rates or over long time horizons.
What is the Rule of 72?▼
The Rule of 72 is a quick mental math shortcut: divide 72 by your annual interest rate to estimate how many years it will take to double your money. For example, at 7% annual return, your investment doubles roughly every 72 ÷ 7 = 10.3 years.
How do monthly contributions affect compound interest?▼
Regular monthly contributions dramatically accelerate compound growth. Each contribution earns its own compound interest from the day it's added, so starting contributions early and keeping them consistent is often more impactful than increasing the initial lump-sum deposit.
Try the calculator
See exactly how your money grows with our interactive compound interest calculator — with charts, monthly breakdowns, and shareable links.
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