Compound Interest Formula: How Your Money Grows

What Is Compound Interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which only applies to the principal), compound interest causes your money to grow exponentially over time. Albert Einstein reportedly called it "the eighth wonder of the world."

The Compound Interest Formula

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

Where:

• A = final amount (principal + interest)
• P = principal (initial investment)
• r = annual interest rate (decimal)
• n = number of times interest is compounded per year
• t = number of years

Example Calculation

You invest $10,000 at 5% annual interest compounded monthly for 10 years.

A = 10,000 × (1 + 0.05/12)^(12 × 10)
A = 10,000 × (1.004167)^120
A = 10,000 × 1.6470
A = $16,470.09

Your $10,000 grew to $16,470 — earning $6,470 in interest without adding any additional money. With simple interest, you would have earned only $5,000 ($500/year × 10 years).

How Compounding Frequency Affects Growth

The more frequently interest compounds, the more you earn. Here is $10,000 at 5% for 10 years with different compounding frequencies:

• Annually (n=1): $16,288.95
• Quarterly (n=4): $16,436.19
• Monthly (n=12): $16,470.09
• Daily (n=365): $16,486.65

The difference between annual and daily compounding is about $198 on this example. While small here, it becomes significant with larger principals or longer time horizons.

The Power of Time

Time is the most important factor in compounding. Consider two investors:

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

At 7% annual return, Investor A ends up with approximately $338,000 at age 65, while Investor B ends up with about $227,000. Despite contributing three times less, Investor A wins because of the extra 10 years of compounding. This is why starting early matters so much.

The Rule of 72

A quick way to estimate how long it takes to double your money:

Years to double ≈ 72 / Interest Rate

At 6% interest, your money doubles in approximately 12 years. At 8%, it takes about 9 years.

Compound Interest Works Against You Too

Credit card debt, student loans, and other borrowing also compound — but against you. A $5,000 credit card balance at 20% APR, paying only the minimum, can take over 20 years to pay off and cost more in interest than the original balance.

Conclusion

Compound interest is the single most powerful concept in personal finance. Start investing early, let time work for you, and avoid high-interest debt. Run your own scenarios with our Compound Interest Calculator to see exactly how your wealth can grow.