Simple interest is calculated only on the original principal — it grows linearly. Compound interest is calculated on principal plus accumulated interest — it grows exponentially. For savings, compound interest is your best friend. For debt, it's your biggest enemy.
What Is Simple Interest?
Simple interest is calculated only on the original principal amount. The formula is straightforward: I = P × r × t, where P is principal, r is the annual rate, and t is time in years. Interest earned in year 1 is the same as interest earned in year 10.
Simple interest is used in some auto loans, short-term personal loans, and treasury bills. It's predictable and easy to calculate, but it doesn't capture the growth potential of reinvested earnings.
What Is Compound Interest?
Compound interest is calculated on the principal plus any interest that has already been earned. The formula is: A = P(1 + r/n)nt, where n is the number of compounding periods per year. Each period, you earn interest on your interest — creating exponential growth over time.
Savings accounts, CDs, bonds, and investment returns all compound. Credit card debt and most mortgages also compound, which is why unpaid balances can grow so quickly.
Side-by-Side Comparison
| $10,000 at 8% for… | Simple Interest | Compound Interest (annual) |
|---|---|---|
| 5 years | $14,000 | $14,693 |
| 10 years | $18,000 | $21,589 |
| 20 years | $26,000 | $46,610 |
| 30 years | $34,000 | $100,627 |
| Total interest earned (30yr) | $24,000 | $90,627 |
After 30 years, compound interest earns 3.8× more than simple interest on the same principal at the same rate.
When Each Type Applies
- Some auto loans and personal loans
- Treasury bills and certain bonds
- Short-term loans between individuals
- Interest-only mortgages (interest portion)
- Savings accounts and CDs
- Investment accounts (stocks, funds)
- Credit card balances
- Mortgages and student loans
- Any reinvested dividends or earnings
Real-World Example
$10,000 invested at 8% for 20 years with different compounding frequencies:
Annual compounding: $46,610
Monthly compounding: $49,268
Daily compounding: $49,530
More frequent compounding earns more. Monthly vs annual adds $2,658 over 20 years. Daily adds another $262 beyond monthly — diminishing returns as frequency increases.
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Frequently Asked Questions
Why is compound interest called the eighth wonder of the world?
This quote is often attributed to Albert Einstein (though debated). It refers to the exponential growth effect: over long periods, compound interest turns small contributions into massive sums. A $500/month investment at 8% for 40 years grows to over $1.7 million.
Do banks use simple or compound interest?
Most bank savings accounts, CDs, and money market accounts use compound interest (typically compounded daily or monthly). Some short-term instruments like T-bills use simple interest.
How does compound interest work on debt?
When you carry a credit card balance, interest compounds on the unpaid balance plus previously accrued interest. A $5,000 balance at 24% APR, paying only minimums, can take 20+ years to pay off and cost $8,000+ in interest.
What is the Rule of 72?
Divide 72 by your interest rate to estimate how many years it takes to double your money with compound interest. At 8%, your money doubles in approximately 72 ÷ 8 = 9 years.
Is continuous compounding significantly better than daily?
The difference between daily and continuous compounding is negligible in practice. On $10,000 at 8% for 20 years, continuous compounding yields about $49,530 vs daily at $49,527 — a $3 difference.