Compound Interest Formula Explained

This reference explains the Compound Interest formula used by our free Compound Interest Calculator. Use it to understand variables, units, and common mistakes before you calculate.

The formula

A = P(1 + r/n)^(nt) + contributions with compound growth

Variables and units

• P — Principal (initial investment) ($)
• r — Annual interest rate (decimal)
• n — Compounding periods per year (integer)
• t — Time in years (years)

Worked example

Inputs: $10,000 principal, 7% annual rate, compounded monthly, 10 years

1. A = P(1 + r/n)^(nt)
2. A = 10,000 × (1 + 0.07/12)^(12×10)
3. A = 10,000 × (1.005833)^120
4. A ≈ $20,096.61

Result: Final balance ≈ $20,097 (roughly double the initial investment)

When to use this formula

Use this formula when you need a quick compound interest estimate with values you already know. Our Compound Interest Calculator applies the same relationship automatically so you can verify handwritten work.

Common mistakes

• Confusing APR with APY
• Ignoring contribution timing (beginning vs end of period)
• Forgetting that higher compounding frequency increases effective yield

Frequently asked questions