Compound Interest Explained: How It Works and Why It Matters

Compound interest is interest earned on interest. Unlike simple interest, which is charged only on the original principal, compounding reinvests each period’s earnings so the base grows — and the growth accelerates over time. Albert Einstein is often quoted (apocryphally) as calling it the most powerful force in the universe; whether or not he said it, the math is unambiguous.

The Formula

A = P × (1 + r/n)^(n×t)

• A = final amount
• P = principal (starting amount)
• r = annual interest rate as a decimal
• n = number of compounding periods per year
• t = number of years

The exponent n×t is what creates the “interest on interest” effect: the rate is applied to a growing base, not a fixed one.

Worked Example

Invest $10,000 at 6% annual interest, compounded monthly (n = 12), for 20 years:

A = 10,000 × (1 + 0.06/12)^(12×20) = 10,000 × (1.005)^240 ≈ $33,102

That is $23,102 in interest — more than double the original principal. The same $10,000 at 6% simple interest would earn only $12,000 over 20 years.

Why Compounding Frequency Matters

The more often interest compounds, the faster money grows:

Daily compounding beats annual by about $1,100 on this example — meaningful, but smaller than the gap between simple and compound interest.

The Rule of 72

A quick mental shortcut: divide 72 by the annual rate to estimate doubling time.

• At 3% → doubles in ~24 years
• At 6% → doubles in ~12 years
• At 9% → doubles in ~8 years

The Rule of 72 is why starting early matters more than chasing a slightly higher rate. Someone who starts saving at 25 and stops at 35 can end up with more than someone who starts at 35 and saves twice as long — because the early money has decades to compound.

Compound Interest Cuts Both Ways

Compounding is also why debt is dangerous. A credit card charging 24% APR, compounded daily on an unpaid balance, grows at a rate that quickly overwhelms minimum payments. The same formula that builds wealth in a savings account builds debt on a card.

Use the Interest Calculator to compare simple vs. compound growth for your own numbers.