How to Calculate Compound Interest (Formula + Examples)

Compound interest is the most powerful force in personal finance — it is interest earning interest on interest. Understanding it helps you both grow savings faster and avoid costly debt traps.

The Compound Interest Formula

A = P × (1 + r/n)^(n×t)

• A = Final amount (principal + interest)
• P = Principal (starting amount)
• r = Annual interest rate (as a decimal, e.g., 5% = 0.05)
• n = Compounding frequency per year (monthly = 12, daily = 365)
• t = Time in years

Example: Savings Account

You invest $10,000 at 6% annual interest, compounded monthly, for 10 years.

A = 10,000 × (1 + 0.06/12)^(12×10)
A = 10,000 × (1.005)^120
A = 10,000 × 1.8194
A = $18,194

Your $10,000 grew to $18,194. You earned $8,194 in interest — more than 80% of your original investment.

How Compounding Frequency Affects Growth

Same example ($10,000 at 6% for 10 years), different compounding frequencies:

• Annual compounding: $17,908
• Monthly compounding: $18,194
• Daily compounding: $18,221

The difference between monthly and daily is small. The big jump is from annual to monthly — frequent compounding matters most at higher interest rates and longer time periods.

The Rule of 72

A quick mental shortcut: divide 72 by the annual interest rate to estimate how many years to double your money.

• At 6%: 72 ÷ 6 = 12 years to double
• At 8%: 72 ÷ 8 = 9 years to double
• At 12%: 72 ÷ 12 = 6 years to double

Compound Interest on Debt

Compound interest works against you on debt. A credit card with 24% APR compounded daily:

If you carry a $3,000 balance for 3 years without paying it off:
A = 3,000 × (1 + 0.24/365)^(365×3) = 3,000 × 2.054 = $6,163

Your $3,000 debt more than doubled in 3 years. Minimum payments often barely cover interest, keeping you in debt indefinitely.

The Time Factor: Why Starting Early is Everything

Investor A starts at age 25, invests $5,000/year for 10 years, then stops. Total invested: $50,000.
Investor B starts at age 35, invests $5,000/year for 30 years. Total invested: $150,000.
Both earn 7% annually.

At age 65:
Investor A: $602,070 (invested $50K)
Investor B: $472,304 (invested $150K)

Investor A invested 1/3 as much but ended up with more — solely because of the extra 10 years of compounding.