Quick answer
Compound interest formula: A = P(1 + r/n)^(nt). Example: $10,000 at 8% compounded monthly for 10 years = $22,196 — earning $12,196 in interest, more than doubling the original principal.
How to use this calculator
Enter your Principal (starting amount), Annual Interest Rate as a percentage, and Time Period in years. The Compounding Frequency defaults to 12 (monthly) — change it to 1 for annual, 4 for quarterly, 365 for daily, or any other value. The calculator shows future value, total interest earned, and a year-by-year growth table (up to 20 years).
Compound interest formula
The compound interest formula calculates the future value of a lump-sum investment growing at a constant rate:
$$A = P\left(1 + \frac{r}{n}\right)^{nt}$$
Where:
- A = future value (the end balance)
- P = principal (the starting amount)
- r = annual interest rate as a decimal (e.g., 8% = 0.08)
- n = number of compounding periods per year (12 = monthly, 365 = daily)
- t = time in years
For continuously compounding interest — where n approaches infinity — the formula simplifies to:
$$A = Pe^{rt}$$
Where e ≈ 2.71828 is Euler's number. Continuous compounding is used in theoretical finance and derivatives pricing; it produces slightly more interest than daily compounding.
Compound vs. simple interest
Simple interest applies only to the original principal. Compound interest applies to the principal plus all previously accumulated interest — creating exponential growth instead of linear growth.
$$A_{\text{simple}} = P(1 + rt)$$
| $10,000 at 8% | 5 Years | 10 Years | 20 Years | 30 Years |
|---|---|---|---|---|
| Simple interest | $14,000 | $18,000 | $26,000 | $34,000 |
| Compound (annual) | $14,693 | $21,589 | $46,610 | $100,627 |
| Compound (monthly) | $14,898 | $22,196 | $49,268 | $109,882 |
The gap between simple and compound interest widens dramatically over long time horizons. At 30 years, monthly compounding produces more than three times the balance of simple interest on the same principal and rate.
Compounding frequency
More frequent compounding produces a slightly higher effective annual rate (EAR), also called the Annual Equivalent Rate (AER). The effective annual rate at a 10% nominal rate:
| Frequency | n (periods/year) | Effective Annual Rate | $10,000 after 1 year |
|---|---|---|---|
| Annually | 1 | 10.000% | $11,000 |
| Semi-annually | 2 | 10.250% | $11,025 |
| Quarterly | 4 | 10.381% | $11,038 |
| Monthly | 12 | 10.471% | $11,047 |
| Weekly | 52 | 10.506% | $11,051 |
| Daily | 365 | 10.516% | $11,052 |
| Continuously | ∞ | 10.517% | $11,052 |
The difference between monthly and daily compounding is less than $5 on $10,000 per year. The meaningful decision is between annual compounding (e.g., some bonds) and more frequent compounding (savings accounts, most mortgages).
Worked examples
| Scenario | Principal | Rate | Frequency | Years | Future Value | Interest Earned |
|---|---|---|---|---|---|---|
| Retirement savings | $50,000 | 7% | Monthly | 30 | $380,613 | $330,613 |
| College fund | $20,000 | 6% | Quarterly | 18 | $58,045 | $38,045 |
| High-yield savings | $5,000 | 4.5% | Daily | 5 | $6,252 | $1,252 |
| Business investment | $100,000 | 10% | Annual | 10 | $259,374 | $159,374 |
Rule of 72 — quick doubling estimate
The Rule of 72 estimates how many years it takes to double an investment at a given annual rate: divide 72 by the interest rate percentage.
$$t = \frac{\ln 2}{n \cdot \ln\!\left(1 + \frac{r}{n}\right)} \approx \frac{72}{r\%}$$
| Annual Rate | Rule of 72 estimate | Exact doubling time |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
The rule also works in reverse: if prices double every 9 years, implied inflation is roughly 72 / 9 = 8% per year. It is a mental math shortcut accurate to within 1–2% for rates between 3% and 15%.
Frequently asked questions
What is compound interest?
Compound interest is interest calculated on both the original principal and all previously earned interest. Because interest earns interest, balances grow exponentially rather than linearly — this is the core mechanism behind long-term wealth accumulation.
What is the compound interest formula?
A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the annual rate as a decimal, n is compounding periods per year, and t is years. For monthly compounding at 8% on $10,000 for 10 years: A = 10,000 × (1 + 0.08/12)^(120) = $22,196.
How does compounding frequency affect interest?
More frequent compounding yields slightly more interest. At 10% on $10,000 for one year: annual compounding = $11,000; monthly = $11,047; daily = $11,052. The difference between monthly and daily is negligible. The more important factor is starting early — time has a much larger effect than compounding frequency.
What is the Rule of 72?
Divide 72 by your annual interest rate to estimate the years needed to double your money. At 6%: 72 / 6 = 12 years. At 9%: 72 / 9 = 8 years. This is an approximation; the exact time is ln(2) / [n × ln(1 + r/n)].
What is the difference between compound and simple interest?
Simple interest applies only to the original principal: A = P(1 + rt). Compound interest applies to principal plus accumulated interest. On $10,000 at 8% for 30 years: simple interest = $34,000 total; compound monthly = $109,882 — more than 3× as much.
What does compounding monthly vs. annually mean?
Monthly compounding (n=12) means interest is calculated and added to the balance 12 times per year, at 1/12 of the annual rate each time. Annual compounding (n=1) adds interest once per year at the full annual rate. Monthly compounding produces a higher effective annual rate and a larger balance over time.