How to Calculate Compound Interest: The Power of Compounding

What Is Compound Interest?

Compound interest is often called the "eighth wonder of the world" — and for good reason. Unlike simple interest, which is calculated only on the original principal, compound interest is calculated on both the principal and the accumulated interest from previous periods. This creates a snowball effect where your money grows exponentially over time.

The Compound Interest Formula

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

Where:

• A = Final amount (principal + interest)
• P = Principal (initial investment)
• r = Annual interest rate (as a decimal)
• n = Number of times interest compounds per year
• t = Number of years

Step-by-Step Example

Let's say you invest $10,000 at 7% annual interest, compounded monthly, for 20 years:

1. P = $10,000
2. r = 0.07
3. n = 12 (monthly compounding)
4. t = 20 years
5. A = $10,000 × (1 + 0.07/12)^(12×20)
6. A = $10,000 × (1.005833)^240
7. A = $10,000 × 4.0387
8. A = $40,387

Your $10,000 grew to over $40,000 — that's $30,387 in interest earned, more than triple your original investment. With simple interest, you would have earned only $14,000 in interest ($10,000 × 0.07 × 20).

How Compounding Frequency Matters

The more frequently interest compounds, the more you earn. Here's how $10,000 at 7% grows over 20 years with different compounding frequencies:

The Rule of 72

The Rule of 72 is a quick mental math shortcut to estimate how long it takes for your money to double. Simply divide 72 by your annual interest rate:

Years to double = 72 ÷ interest rate

At 7% interest, your money doubles in approximately 72 ÷ 7 ≈ 10.3 years. At 10%, it doubles in about 7.2 years. This simple rule helps you quickly evaluate investment opportunities without a calculator.

The Power of Starting Early

Time is the most powerful factor in compound interest. Consider two investors:

• Investor A starts at age 25, invests $200/month for 10 years (until age 35), then stops. Total invested: $24,000.
• Investor B starts at age 35, invests $200/month for 30 years (until age 65). Total invested: $72,000.

Assuming 8% annual returns: Investor A ends up with approximately $509,000 at age 65, while Investor B ends up with approximately $298,000. Investor A invested three times less money but ended up with 70% more — all because of the extra 10 years of compounding.

Practical Tips for Maximizing Compound Interest

• Start as early as possible: Even small amounts grow significantly over decades.
• Be consistent: Regular monthly contributions amplify the compounding effect.
• Reinvest dividends: Don't withdraw your earnings — let them compound.
• Minimize fees: High investment fees eat into your returns and reduce compounding.
• Be patient: Compound interest works best over long time horizons. The real magic happens after 15-20 years.