Compound Interest Explained: How Your Money Grows Over Time

Compound interest is interest calculated on both your original principal and the interest you have already earned. Over time, this creates a snowball effect: your money grows faster and faster the longer it stays invested.

Simple interest vs compound interest

With simple interest, you earn interest only on your original deposit. With compound interest, your interest earns interest too.

Example: you invest $1,000 at 10% per year for 3 years.

• Simple interest: $1,000 x 10% x 3 = $300 earned. Total: $1,300.
• Compound interest (annually): Year 1: $1,100. Year 2: $1,210. Year 3: $1,331. Total: $1,331.
• The difference seems small at 3 years, but over 30 years it becomes enormous.

The compound interest formula

A = P x (1 + r/n) ^ (n x t)

• A: the final amount (principal + interest)
• P: the principal (starting amount)
• r: annual interest rate as a decimal (e.g. 8% = 0.08)
• n: number of times interest compounds per year
• t: number of years

How compounding frequency affects your returns

The more frequently interest compounds, the more you earn. For a $10,000 investment at 8% over 10 years:

• Annually (n=1): $21,589
• Quarterly (n=4): $22,080
• Monthly (n=12): $22,196
• Daily (n=365): $22,253

The differences between monthly and daily compounding are small. The bigger lever is always the interest rate and the time horizon.

The rule of 72

A quick mental math shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 8% annual return, your money doubles roughly every 9 years (72 / 8 = 9). At 6%, every 12 years.

Compound interest working against you

Compound interest works the same way on debt. Credit card debt at 20% annual interest compounds monthly, meaning your balance grows fast if you only make minimum payments. The same math that builds wealth can accelerate debt if left unmanaged.