What Is Compound Interest?
Compound interest means you earn (or owe) interest not only on your original principal, but also on previously accumulated interest. Over years, growth accelerates — the same rate produces larger dollar gains each period because the base is bigger.
This is why starting early matters so much for retirement and why high-interest debt snowballs badly: the effect works for you when saving and against you when borrowing.
Compound Interest Formula
Future value A with periodic compounding:
A = P × (1 + r/n)^(n×t)
| Symbol | Meaning |
|---|---|
| P | Principal (starting amount) |
| r | Annual nominal interest rate (decimal) |
| n | Compounding periods per year |
| t | Time in years |
Example: $5,000 at 6% annual, compounded monthly, for 10 years:
- •
r = 0.06,n = 12,t = 10 - •
A = 5000 × (1 + 0.06/12)^(120) ≈ $9,098
Compare to simple interest on $5,000 only: 5000 × 0.06 × 10 = $3,000 interest — compound on the full balance does better.
Compounding Frequency Matters
At the same nominal annual rate, more frequent compounding yields slightly more return:
- •Annual — interest credited once per year
- •Quarterly — four times per year
- •Monthly — twelve times
- •Daily — 365 times
The limit as compounding becomes continuous uses e^(r×t) — you'll see this in advanced finance.
APY (Annual Percentage Yield) reflects compounding; APR often does not. Savings accounts usually quote APY.
Rule of 72 (Mental Math)
Roughly:
Years to double ≈ 72 / (interest rate in %)
At 8% compounded, money doubles in about 9 years. It's an approximation, not exact — but useful for intuition.
How to Use This Calculator
Enter principal, annual rate, time, contribution (optional), contribution frequency, and compound frequency. You'll see future value, total interest earned, and growth charts where available.
Use conservative rates for long-term planning — past returns don't guarantee future results.