HOW IT WORKS
Simple interest is calculated only on the principal: Interest = Principal × Rate × Time. Compound interest earns interest on interest: A = P(1 + r/n)^(nt). More frequent compounding (daily vs yearly) means more interest earned.
SIMPLE VS COMPOUND INTEREST
Simple Interest: Calculated only on the original principal. Formula: I = P × r × t. Example: $10,000 at 5% for 5 years = $2,500 interest ($500/year × 5). Total: $12,500.
Compound Interest: Interest earns interest. Each period's interest is added to principal, then next period's interest is calculated on the new total. Same example with monthly compounding = $2,834 interest. Total: $12,834.
The Difference: Compound interest earns $334 more than simple interest in this example. The longer the time period and higher the rate, the bigger the difference. This is called the "compound bonus."
COMPOUNDING FREQUENCY EXPLAINED
Annually (n=1): Interest added once per year. Lowest compound effect. $10,000 at 5% for 5 years = $12,763.
Semi-annually (n=2): Interest added twice per year. Same example = $12,801.
Quarterly (n=4): Interest added 4 times per year. Common for bonds. Same example = $12,820.
Monthly (n=12): Interest added 12 times per year. Most common for savings accounts. Same example = $12,834.
Daily (n=365): Interest added every day. Maximum practical compounding. Same example = $12,840.
Key insight: Monthly to daily compounding makes little difference ($6 in this example). The big jump is from annual to monthly.
REAL-WORLD INTEREST RATES
High-yield savings accounts: 4-5% APY (2024). Example: $10,000 at 4.5% = $10,450 after 1 year.
CDs (Certificate of Deposit): 4-5.5% APY. Locked for 6 months to 5 years. Higher rate for longer terms.
Money market accounts: 3-5% APY. Similar to savings but may have check-writing ability.
10-year Treasury bonds: 4-5% (2024). Government-backed, very safe.
Stock market (S&P 500): ~10% average annual return historically. But varies widely year to year.
Credit cards: 20-30% APR. This is interest you PAY, not earn. Avoid carrying balances.
THE POWER OF TIME (RULE OF 72)
Rule of 72: Divide 72 by your interest rate to find how many years to double your money. At 6% rate: 72 ÷ 6 = 12 years to double.
At 3%: 24 years to double. $10,000 becomes $20,000 in 24 years.
At 6%: 12 years to double. $10,000 becomes $20,000 in 12 years, $40,000 in 24 years.
At 10%: 7.2 years to double. $10,000 becomes $20,000 in 7 years, $80,000 in 21 years.
Key insight: Start early. $10,000 invested at 25 at 7% becomes $150,000 by 65. The same $10,000 invested at 45 becomes only $39,000 by 65.