What Is Compound Interest? Formula, Examples & Free Calculator (2026 Guide)

Simple interest pays only on the original principal. Compound interest pays on principal plus all interest earned so far.

Example: $10,000 at 5% simple interest earns $500/year every year — always $500.

$10,000 at 5% compound interest earns $500 in year 1, $525 in year 2 ($10,500 × 5%), $551.25 in year 3, and so on.

After 30 years: simple interest gives you $25,000. Compound interest gives you $43,219 — 73% more from the same rate.

Albert Einstein allegedly called compound interest "the eighth wonder of the world." Whether he said it or not, the math supports the sentiment.

Breaking down each variable:

• A = final amount (principal + interest)
• P = principal (starting amount)
• r = annual interest rate (as a decimal, so 5% = 0.05)
• n = number of times interest compounds per year (12 for monthly, 365 for daily)
• t = number of years

Example: $10,000 at 6% compounded monthly for 20 years:

A = 10,000 × (1 + 0.06/12)^(12×20)

A = 10,000 × (1.005)^240

A = 10,000 × 3.3102

A = $33,102

Your $10,000 more than tripled — and $23,102 of that is pure interest earned on interest.

$10,000 at 6% for 10 years with different frequencies:

• Annual: $17,908
• Semi-annual: $18,061 (+$153)
• Quarterly: $18,140 (+$79)
• Monthly: $18,194 (+$54)
• Daily: $18,221 (+$27)

The difference between annual and monthly compounding is meaningful ($286). Between monthly and daily it's only $27.

In practice, most savings accounts compound daily, and most investment returns compound based on the reinvestment schedule. Focus on the rate and time horizon — frequency is a minor factor.

The classic comparison:

Investor A: Invests $200/month from age 25 to 65 (40 years) at 8% → $702,856

Investor B: Invests $400/month from age 35 to 65 (30 years) at 8% → $589,020

Investor A invests half as much per month but ends up with $113,000 more, because those extra 10 years of compounding on early contributions are incredibly powerful.

Total contributed: A = $96,000, B = $144,000

Interest earned: A = $606,856, B = $445,020

The lesson: start now with whatever you can afford. Time is the one resource you can't buy back.