Understanding Compound Interest

What Is Compound Interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which only grows linearly, compound interest creates exponential growth over time.

The formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual rate, n is the compounding frequency, and t is time in years.

The Power of Compounding

Consider investing $10,000 at 8% annual return. After 10 years you would have about $21,589. After 20 years: $46,610. After 30 years: $100,627. Your money doubled roughly every 9 years without adding a single dollar.

The key insight is that growth accelerates over time. The first $10,000 of gains took about 9 years. The last $10,000 of gains took less than a year. This is why starting early matters more than investing large amounts later.

The Rule of 72

The Rule of 72 is a quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes for your money to double. At 6%, your money doubles in roughly 12 years. At 10%, it doubles in about 7.2 years.

• 72 / 4% = 18 years to double
• 72 / 6% = 12 years to double
• 72 / 8% = 9 years to double
• 72 / 12% = 6 years to double

Compounding Frequency Matters

Interest can compound annually, quarterly, monthly, or even daily. More frequent compounding produces slightly higher returns. On $10,000 at 8% for 10 years, annual compounding yields $21,589, while monthly compounding yields $22,196 — a difference of about $607.

Compound Interest Works Against You Too

Credit card debt typically compounds daily at high rates. A $5,000 balance at 22% APR, paying only the minimum, can take over 20 years to pay off and cost more than $10,000 in interest. Understanding compounding helps you see why paying off high-interest debt should be a top priority.

Use our compound interest calculator to see how your savings or debts will grow over time.