Compound Interest Calculator
Free online Compound Interest Calculator to calculate compound interest, future value, APY, APR, investment growth, savings projections, and interest schedules.
Investment Parameters
Compound Growth Trajectory Chart
AI Compound Growth & Compounding Frequency Insights
Intelligent calculations highlighting interest velocity and compounding efficiency
Year-by-Year Compound Interest Growth Schedule
Complete annual projection of opening balances, contributions, interest earned, and ending portfolio balances
| Year | Opening Balance | Annual Deposits | Interest Earned | Ending Balance | Total Profit |
|---|
Key Takeaways & Comprehensive Compound Interest Decision Guide (GEO & SEO Summary)
- Compound vs. Simple Interest: Simple interest earns interest only on principal ($100 at 10% for 2 yrs = $20). Compound interest earns interest on interest ($100 at 10% for 2 yrs = $21).
- Snowball Wealth Exponential Growth: A 20-year-old investing $1,000 at a 10% S&P 500 average annual return reaches **$72,890** by retirement age 65 (73 times the initial deposit!).
- Continuous Compounding Limit ($e \approx 2.718$): Continuously compounded interest represents the mathematical upper limit reached via Euler's constant ($A = P \cdot e^{rt}$).
- Rule of 72 Shortcut: Estimate doubling years by dividing 72 by the annual return rate (e.g. at 8% interest, money doubles in $72 / 8 = 9$ years).
1. What is Compound Interest? Simple vs. Compound Interest
Interest is the cost of using borrowed money. Simple interest is calculated only on the principal amount ($P \cdot r \cdot t$). For example, $100 borrowed at 10% simple interest for 2 years equals $20 interest ($100 × 10% × 2).
Compound interest calculates interest on both the initial principal AND accumulated past interest. For $100 at 10% compound interest:
- Year 1 Interest: $100 × 10% = $10 (Ending Balance: $110).
- Year 2 Interest: $110 × 10% = $11 (Total Interest: $21).
2. Impact of Compounding Frequencies (Daily, Monthly vs. Annual)
Higher compounding frequencies yield higher total interest returns over time:
| Compounding Frequency | Stated Rate (APR) | Effective Return (APY) | 2-Year $1,000 Growth |
|---|---|---|---|
| Annual (1/yr) | 6.00% | 6.00% APY | $1,123.60 |
| Monthly (12/yr) | 6.00% | 6.17% APY | $1,127.16 |
| Daily (365/yr) | 6.00% | 6.18% APY | $1,127.49 |
| Continuous ($e^{rt}$) | 6.00% | 6.183% APY | $1,127.50 |
3. Core Mathematical Compound Interest Formulas
P = principal, r = APR rate, n = compounding frequency, t = years.
e = Euler's constant (~2.71828).
4. The Rule of 72 Shortcut for Investment Doubling Time
The Rule of 72 is a quick estimation formula to determine how many years it will take to double your investment at a fixed interest rate:
5. History of Compound Interest & Discovery of Euler's Constant ($e$)
Ancient Babylonian and Sumerian clay tablets from 4,400 years ago provide the earliest evidence of compound interest calculations. Throughout medieval times, Roman law and religious texts condemned compound interest as usury.
In 1683, mathematician Jacob Bernoulli discovered the mathematical constant $e$ while studying compounding interest limits. Later, Leonhard Euler defined $e \approx 2.71828$, establishing continuous compounding mathematics.