About the Compound Interest Calculator
Compound interest is the fundamental engine behind long-term wealth creation. Unlike simple interest—which produces fixed, linear returns calculated exclusively on the original deposit—compounding reinvests every dollar of earned interest so that future cycles earn interest on top of past interest.
1. The Core Compounding Formula
A = P(1 + r/n)nt
- A: Final maturity balance
- P: Initial principal investment
- r: Annual nominal interest rate (decimal)
- n: Compounding intervals per year
- t: Investment duration in years
2. Effective Annual Yield (APY)
APY = (1 + r/n)n - 1
Measures true annualized percentage yield. For instance, a 10% rate compounded monthly yields an effective annual return of 10.47%.
Compounding Frequency Comparison on $10,000 at 8% for 10 Years
| Compounding Interval | Cycles / Year ($n$) | Effective APY | Final Maturity Balance |
|---|---|---|---|
| Annually | 1 | 8.00% | $21,589.25 |
| Semi-Annually | 2 | 8.16% | $21,911.23 |
| Quarterly | 4 | 8.24% | $22,080.40 |
| Monthly | 12 | 8.30% | $22,196.40 |
| Daily | 365 | 8.33% | $22,253.46 |