Compound interest is the interest earned on both the initial principal and previously accumulated interest. Unlike simple interest, which only applies to the original amount, compound interest accelerates wealth growth over time through the power of reinvestment.

The compound interest formula is: A = P(1 + r/n)^(nt)

Where:

• A = Final amount
• P = Principal (initial investment)
• r = Annual interest rate (in decimal form)
• n = Number of times interest compounds per year
• t = Time in years

For example, investing $1,000 at 5% annual interest compounding monthly for 5 years:

• Principal (P) = $1,000
• Rate (r) = 0.05
• Compounds (n) = 12 (monthly)
• Time (t) = 5 years

Final amount = $1,000(1 + 0.05/12)^(12×5) = $1,283.36

Common compounding frequencies:

• Daily
• Weekly
• Monthly
• Quarterly
• Annually

Compound interest typically applies to:

• Savings accounts
• Investment accounts
• Some loans and credit cards
• Retirement accounts
• Certificates of deposit (CDs)

The power of compound interest becomes more apparent over longer time periods. Starting to save and invest early allows more time for compound interest to work, potentially leading to significantly larger returns compared to simple interest investments.

Key factors affecting compound interest:

• Initial investment amount
• Interest rate
• Compounding frequency
• Time invested
• Regular contributions (if any)

Understanding compound interest is crucial for both saving and borrowing decisions, as it can work for or against you depending on whether you're earning or paying interest.

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