How to Calculate Compound Interest: Formula, Examples, and Calculator

Compound Interest Formula

The compound interest formula calculates the future value of an investment based on exponential growth. The standard formula is:

A = P (1 + r/n)^(nt)

Where:

• A = Final amount after interest
• P = Initial principal (your starting deposit)
• r = Annual interest rate (in decimal form: 7% = 0.07)
• n = Number of times interest compounds per year
• t = Number of years

Step-by-Step Calculation Example

Problem: You invest $5,000 at 6% annual interest compounded monthly. What's the value after 10 years?

1. P = $5,000, r = 0.06, n = 12, t = 10
2. A = 5000 × (1 + 0.06/12)^(12 × 10)
3. A = 5000 × (1.005)^120
4. A = 5000 × 1.8194
5. A = $9,097

Your $5,000 grew to over $9,000 without adding a single dollar beyond the initial deposit. The interest earned: $4,097.

With Monthly Contributions

If you add regular contributions, the formula extends to:

A = P(1+r/n)^(nt) + PMT × [((1+r/n)^(nt) - 1) / (r/n)]

Where PMT = monthly contribution amount. This is the exact formula used by our Compound Interest Calculator.

Quick Calculation: The Rule of 72

Divide 72 by your interest rate to estimate doubling time. At 8%: 72 ÷ 8 = 9 years to double. At 12%: 72 ÷ 12 = 6 years. This rule works for any rate between 2% and 30%.

Simple vs Compound Interest Comparison

On $10,000 at 7% over 30 years:

• Simple interest: $10,000 + ($700 × 30) = $31,000
• Compound interest (annual): $10,000 × (1.07)^30 = $76,123
• Compound interest (monthly): $10,000 × (1.00583)^360 = $81,165

The difference between simple and compound interest over 30 years is over $50,000 — that's the power of compounding.

Use Our Calculator

Instead of doing complex math by hand, use our free Compound Interest Calculator. It handles monthly contributions, shows a growth chart, and gives you instant results for any scenario. For retirement planning, try our Retirement Calculator or SIP Calculator for systematic investing.