Understanding Compound Interest
Albert Einstein famously called compound interest the "eighth wonder of the world". Unlike simple interest, which is calculated only on the principal amount, compound interest is calculated on the principal plus the accumulated interest.
How the Formula Works
The standard formula for compound interest is:
- A: The future value of the investment/loan.
- P: The principal investment amount.
- r: The annual interest rate (decimal).
- n: The number of times that interest is compounded per unit t.
- t: The time the money is invested or borrowed for.
Why It Matters
For investors, compounding is your best friend. A small sum invested early can grow into a fortune over decades purely due to the "snowball effect" of interest earning interest. For borrowers, however, it can be dangerous, as debt can swell rapidly if not paid off.
A Quick Worked Example
Suppose you invest $5,000 at an 8% annual rate, compounded monthly, for 10 years. Plugging into the formula gives A = 5000 × (1 + 0.08/12)^(12×10) ≈ $11,098. You more than doubled your money without adding a single extra dollar. Compare that to simple interest over the same period (5000 × 1.8 = $9,000) and you can see compounding alone earned an extra $2,098.
The Role of Compounding Frequency
How often interest is added matters. The same 8% rate compounded daily grows faster than compounded annually, because interest is calculated and reinvested more often. Over a 20–30 year horizon, the difference between daily and annual compounding can add up to several extra percentage points of total growth.
The Rule of 72
Want a fast mental estimate of how long it takes to double your money? Divide 72 by your interest rate. At 8%, that's roughly 9 years — which lines up almost exactly with the worked example above.