The Compound Interest Formula
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods — which is what makes it grow faster than simple interest over time. The formula is:
A = P × (1 + r/n)^(n×t)
Where:
- A = the final (maturity) amount
- P = the principal (initial investment)
- r = the annual interest rate (as a decimal)
- n = the number of times interest compounds per year
- t = the number of years
Why Compounding Frequency Matters
The more frequently interest compounds, the faster your money grows — because interest starts earning interest sooner. Monthly compounding will always yield a slightly higher return than annual compounding at the same nominal rate, and daily compounding yields marginally more than monthly.
The Power of Time
Compound interest rewards patience disproportionately: doubling your investment horizon more than doubles your total growth, because each additional year compounds on an already-larger base. This is why starting to invest early — even with smaller amounts — often outperforms starting later with larger amounts.
Common Applications
- Projecting the future value of fixed deposits, recurring deposits, and savings accounts
- Estimating long-term mutual fund or retirement account growth
- Understanding how compounding debt (like credit card interest) can grow if left unpaid