How Simple and Compound Interest Work

Interest is the cost of borrowing money (for loans) or the reward for saving/investing money (for deposits). It is expressed as a percentage rate, usually annual (APR). There are two fundamental types: simple interest and compound interest. Understanding the difference is crucial for making informed financial decisions about savings accounts, loans, mortgages, and investments.

Simple Interest = Principal x Rate x Time Simple interest is calculated only on the original principal amount. The interest earned each period is constant. Example: $10,000 at 5% for 3 years - Year 1: $10,000 x 0.05 = $500 - Year 2: $10,000 x 0.05 = $500 - Year 3: $10,000 x 0.05 = $500 - Total Interest: $1,500 - Total Amount: $11,500 Simple interest is used for short-term loans, car loans, and some certificates of deposit.

A = P(1 + r/n)^(nt) Compound interest is calculated on the principal AND the accumulated interest. Interest earns interest, creating exponential growth. Example: $10,000 at 5% compounded annually for 3 years - Year 1: $10,000 x 1.05 = $10,500 - Year 2: $10,500 x 1.05 = $11,025 - Year 3: $11,025 x 1.05 = $11,576.25 - Total Interest: $1,576.25 (vs $1,500 with simple interest) The difference grows dramatically over time. Over 30 years, $10,000 at 5% becomes: - Simple: $25,000 - Compound: $43,219

$10,000 at 5% for 10 years with different compounding: - Annually: $16,288.95 - Semi-annually: $16,386.16 - Quarterly: $16,436.19 - Monthly: $16,470.09 - Daily: $16,486.65 - Continuously: $16,487.21 More frequent compounding means higher returns, but the marginal benefit decreases. The jump from annual to monthly is significant; from monthly to daily is minimal.

A quick way to estimate how long it takes to double your money: Years to Double = 72 / Interest Rate Examples: - At 6%: 72 / 6 = 12 years - At 8%: 72 / 8 = 9 years - At 10%: 72 / 10 = 7.2 years - At 12%: 72 / 12 = 6 years This rule works well for rates between 2% and 15%. For higher rates, use the Rule of 69.3 for better accuracy.