Compound Interest Calculator
Simulate the exponential power of compounding interest over time. Factor in initial principal, recurring monthly contributions, investment horizons, and custom compounding frequencies to project your future portfolio net worth.
The Mathematics of Compound Growth: How Money Multiplies
Compound interest is the process where interest is earned not only on the initial principal sum, but also on the accumulated interest of prior compounding periods. Often described as "interest on interest", it creates a hyperbolic growth curve that accelerates dramatically over extended multi-decade timeframes.
The Master Compound Interest Equation
When incorporating regular recurring additions (annuities), the future value formula combines lump-sum compounding with the future value of a series:
Where:
- A = Final accumulated balance (Future Value).
- P = Initial principal lump sum.
- PMT = Monthly recurring contribution deposit.
- r = Nominal annual interest rate in decimal form (e.g. 8% = 0.08).
- n = Compounding frequency per calendar year (12 for monthly, 365 for daily).
- t = Number of elapsed years invested.
The Rule of 72: Instant Mental Compounding
The Rule of 72 is a reliable mental shortcut for approximating how many years it will take an investment to double at a fixed annual rate of return:
For example, at a standard historical index fund return of 8% per year, your capital doubles approximately every 9 years (72 / 8 = 9). Over a 36-year career, a single lump sum doubles four consecutive times—multiplying your purchasing power by 16x.
How Compounding Frequency Impacts Returns
More frequent compounding cycles slightly increase your Effective Annual Rate (EAR) because interest is reinvested sooner:
- Annual (n=1): $10,000 at 8% yields $10,800.00 after 1 year.
- Quarterly (n=4): $10,000 at 8% yields $10,824.32 after 1 year.
- Monthly (n=12): $10,000 at 8% yields $10,829.99 after 1 year.
- Daily (n=365): $10,000 at 8% yields $10,832.78 after 1 year.