How to Calculate Compound Interest: The Formula Explained Simply

Albert Einstein allegedly called compound interest the 'eighth wonder of the world.' Whether or not he said it, the math is undeniably powerful. Understanding compound interest helps you make better investment decisions, choose the right savings accounts, and understand why starting early matters so much. Here's the formula explained simply, with real examples.

What Is Compound Interest?

Simple interest pays you interest only on your original principal. Compound interest pays you interest on your principal AND on the interest you've already earned. That 'interest on interest' effect creates exponential growth over time — the longer the time horizon, the more dramatic the difference.

The Compound Interest Formula

The standard compound interest formula is: A = P(1 + r/n)^(nt)

• A = Final amount (principal + interest)
• P = Principal (starting amount)
• r = Annual interest rate (as a decimal — 7% = 0.07)
• n = Number of times interest compounds per year
• t = Time in years

Example: $10,000 invested at 7% annually for 20 years, compounded once per year: A = 10,000 × (1 + 0.07/1)^(1×20) = 10,000 × (1.07)^20 = 10,000 × 3.87 = $38,700. Your $10,000 almost quadrupled with zero additional contributions.

How Compounding Frequency Affects Returns

The more often interest compounds, the more you earn. Using the same $10,000 at 7% for 20 years:

• Annual compounding: $38,697
• Monthly compounding: $40,064
• Daily compounding: $40,138
• Continuous compounding: $40,149

The difference between annual and daily compounding on this example is about $1,440 over 20 years. For larger amounts and longer periods, the difference grows substantially. Most investment accounts compound daily or monthly.

The Rule of 72

The Rule of 72 is a quick mental math shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 6%: 72/6 = 12 years to double. At 8%: 72/8 = 9 years. At 12%: 72/12 = 6 years. It's not exact, but it's remarkably accurate for rates between 5% and 15%.

Why Starting Early Matters So Much

Consider two investors. Investor A puts $5,000/year into the market from age 25 to 35 (10 years, $50,000 total), then stops completely. Investor B waits until 35 and puts $5,000/year until retirement at 65 (30 years, $150,000 total). At 7% annual return: Investor A has ~$602,000 at 65. Investor B has ~$567,000. Investor A invested less money but won by starting early.