What Is Compound Interest? Definition, Formula, and Examples

Compound interest is the reason long-term investing works: you earn returns on your original investment and on previously earned returns.

If you want to see compounding with contributions and time, start with:

• Compound Interest Calculator
• Future Value Calculator

Simple interest vs compound interest

• Simple interest: interest is calculated only on the original principal.
• Compound interest: interest is calculated on principal plus accumulated interest.

Compounding can be daily, monthly, quarterly, or annually. In practice, contribution rate and time horizon usually matter more than the exact compounding frequency.

The compound interest formula

The standard formula for a single lump sum is:

FV = PV × (1 + r)^n

Where:

• PV = present value (starting amount)
• r = rate per period
• n = number of periods

With monthly contributions, you’re effectively combining a lump sum growth calculation plus a contribution stream. The Future Value Calculator models both.

Example: $10,000 growing at 7% for 20 years

Using the formula:

• PV = $10,000
• r = 7% per year
• n = 20 years

FV ≈ $10,000 × (1.07)^20 ≈ $38,697

If you add monthly contributions (like $300/month), the final balance can be much higher. Try it in the Compound Interest Calculator.

Why time matters more than timing

The biggest lever in compounding is usually time. Even a modest contribution rate can compound into a large ending balance when you give it enough years.

If you want a quick rule-of-thumb for doubling time, use the Rule of 72 Calculator.

Don’t ignore inflation

A 7% nominal return with 3% inflation is closer to a ~4% real return. Use the Inflation Calculator to understand buying power, and consider “real return” when planning long horizons.

FAQ

Does compounding happen in savings accounts too?

Yes. Savings accounts can compound interest, but the rate is often lower than long-term investment returns.

What return rate should I assume?

For planning, many people model a range (for example 5%–8%). Use conservative assumptions when making long-term decisions.

Is compound interest guaranteed?

No. Market returns vary year to year. Compound interest describes the math of reinvesting gains, not a promise of returns.

How often should I contribute?

Consistency matters. Monthly contributions are common and easy to model with the Future Value Calculator.

How do I compare two investments?

Compare ending value, total contributions, and a standardized growth rate like CAGR. Use the Investment Return Calculator and CAGR Calculator.