Compound Interest Explained: The Formula, the Rule of 72, and Why Time Matters

Simple interest is paid only on the original amount. Compound interest is paid on the original amount plus the interest already earned, so the growth builds on itself. Over long periods the difference is dramatic.

The formulas

Simple:    A = P x (1 + r x t)
Compound:  A = P x (1 + r/n)^(n x t)

P = starting amount   r = annual rate (as a decimal)
t = years             n = compounding periods per year

A worked example

Invest 10,000 at 7% per year for 20 years:

• Simple interest: 10,000 x (1 + 0.07 x 20) = 24,000.
• Compounded annually: 10,000 x 1.07^20 = about 38,697.
• Compounded monthly: 10,000 x (1 + 0.07/12)^240 = about 40,387.

The difference between simple and compound is almost 15,000 on the same rate and time, entirely from earning interest on interest.

Compounding frequency

The more often interest compounds (annually, monthly, daily), the more you earn, but the gains from increasing frequency shrink quickly. Moving from annual to monthly matters more than going from monthly to daily.

The rule of 72

To estimate how long money takes to double, divide 72 by the annual rate in percent. At 6%, 72 / 6 = 12 years (the exact figure is about 11.9). It is a handy mental shortcut that works best for rates between about 4% and 12%.

What this means in practice

• Starting early matters more than starting big; time is the main ingredient.
• Regular contributions add fresh principal that also compounds.
• The same math works against you on debt: credit card balances compound too.
• Fees and taxes reduce the effective rate, so compare after-cost returns.