1. The Mathematics of Exponential Growth
Unlike simple interest (which only calculates returns on the principal), compound interest calculates returns on both the initial principal and the accumulated interest from previous periods.
The standard formula is:
$$A = P \times \left(1 + \frac{r}{n}\right)^{n \times t}$$
- A: Final amount (future value)
- P: Principal investment amount
- r: Annual interest rate (in decimal, e.g. 7% = 0.07)
- n: Compounding frequency per year (12 for monthly, 1 for annually)
- t: Number of years the money is invested
2. The Rule of 72
A fast mental shortcut to estimate how many years it takes to double your money at a fixed compound rate is dividing 72 by the annual interest rate:
Years to Double ≈ 72 ÷ Interest Rate (%)
For example, at an 8% annual return, your capital doubles in approximately 72 ÷ 8 = 9 years.