How Compound Interest Works

The Compound Interest Formula

Compound interest means earning (or paying) interest on both the original principal and the interest already accumulated. The standard formula is:

Where:

• A = Final amount (principal + interest)
• P = Principal (starting amount)
• r = Annual interest rate (as a decimal)
• n = Number of times interest compounds per year
• t = Time in years

Simple vs. Compound Interest

Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously accumulated interest. The difference grows significantly over time.

Example: $10,000 invested at 7% per year for 20 years:

The compound interest result is $14,697 more than simple interest over 20 years — on the same $10,000 initial investment.

How Compounding Frequency Affects Growth

The more frequently interest compounds, the more you earn (or owe). The difference between annual and daily compounding is smaller than most people expect, but it is real.

$10,000 at 7% for 20 years, varying only the compounding frequency:

The Rule of 72

The Rule of 72 is a quick mental math shortcut for estimating how long it takes to double an investment at a given compound interest rate. Divide 72 by the annual interest rate to get the approximate number of years to double.

• At 6%: 72 ÷ 6 = 12 years to double
• At 8%: 72 ÷ 8 = 9 years to double
• At 12%: 72 ÷ 12 = 6 years to double

The Rule of 72 is an approximation. The exact formula confirms: $10,000 at 6% compounded annually doubles to $20,122 in exactly 12.0 years.

Compound Interest on Debt

Compound interest works against you on debt. Credit card balances that compound daily at 20% APR grow rapidly if only minimum payments are made. A $5,000 credit card balance at 20% APR with a $100 minimum payment takes over 9 years to pay off and costs approximately $6,800 in interest — more than the original balance.