The Mechanics of Compound Interest
Compound interest occurs when the interest earned on an investment is reinvested to generate its own interest in subsequent periods. Over long horizons, this compounding creates exponential wealth acceleration.
Core Compounding Formula
Without periodic contributions, future balance $A$ is calculated as:
$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$
Where:
- $P$: Initial principal sum
- $r$: Annual nominal interest rate (in decimal format, e.g. $0.08$)
- $n$: Number of compounding periods per year ($12$ for monthly, $4$ for quarterly)
- $t$: Total investment tenure in years
Adding Periodic Contributions (Annuity Future Value)
When periodic payments ($PMT$) are contributed each month, the additional future value is added via the future value of a series formula:
$$A_{\text{total}} = P \left(1 + \frac{r}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$$