Simple vs Compound Interest: Key Differences
Simple interest is calculated only on the original principal — it grows linearly. Compound interest is calculated on the principal plus accumulated interest — it grows exponentially. The longer the time period, the larger the gap between them.
On $10,000 invested at 5% for 30 years: simple interest gives $25,000 total ($15,000 interest). Compound interest (annual) gives $43,219 total ($33,219 interest). Monthly compounding gives $44,677. The difference is $19,677 — almost twice the original principal in extra growth.
| Property | Simple Interest | Compound Interest |
|---|---|---|
| Formula | I = P × r × t | A = P(1 + r/n)^(nt) |
| Interest earned on | Principal only | Principal + accumulated interest |
| Growth shape | Linear (straight line) | Exponential (curve) |
| Effect of time | Proportional to time | Accelerates over time |
| Compounding frequency | N/A (no compounding) | Annual, monthly, daily, continuous |
| $10K at 5%, 10 years | $5,000 interest → $15,000 | $6,289 interest → $16,289 (annual) |
| $10K at 5%, 30 years | $15,000 interest → $25,000 | $33,219 interest → $43,219 (annual) |
| Common uses | Short-term loans, T-bills, some bonds | Savings accounts, mortgages, investments |
| Benefits investor? | Less | More — earns interest on interest |
| Benefits borrower? | More — pays less interest | Less — pays compounded interest |
Simple Interest — Formula and Calculation
Formula: I = P × r × t. Total Amount: A = P + I = P(1 + rt).
Variables: P = principal (initial amount). r = annual interest rate (as decimal). t = time in years.
Example: $5,000 at 4% for 3 years. I = 5000 × 0.04 × 3 = $600. Total = $5,600. The interest is the same every year: $200/year. This linear growth is the defining characteristic of simple interest.
When simple interest is used: Short-term personal loans. US Treasury bills (T-bills, < 1 year). Car loans (some use Rule of 78s, a simple interest variant). Some payday loans. Credit card promotional periods (0% APR for 12 months). Most straightforward to understand and calculate.
Compound Interest — Formula and Calculation
Formula: A = P(1 + r/n)^(nt). Where n = number of compounding periods per year.
Common compounding frequencies: Annual (n=1). Semi-annual (n=2). Quarterly (n=4). Monthly (n=12). Daily (n=365). Continuous: A = Pe^(rt) (e ≈ 2.71828).
Example (annual compounding): $5,000 at 4% for 3 years. A = 5000 × (1.04)³ = 5000 × 1.12486 = $5,624.32. Interest = $624.32. More than simple interest ($600) by $24.32.
The key mechanism: At the end of Year 1, $200 interest is added to the principal. In Year 2, interest is computed on $5,200 (not $5,000) — earning $208 instead of $200. The extra $8 is "interest on interest." This reinvestment effect compounds over time.
When compound interest is used: Savings accounts and high-yield accounts. Investment accounts (stocks, ETFs, mutual funds). Mortgages and home equity loans. Student loans and most long-term debt. Credit card balances (daily compounding is common).
$10,000 at 5% — Growth Comparison Over 30 Years
The table below shows total account value at each time point, illustrating how compound interest accelerates over time while simple interest grows at a constant $500/year.
| Year | Simple Interest Total | Compound (Annual) | Compound (Monthly) | Advantage (Monthly vs Simple) |
|---|---|---|---|---|
| 1 | $10,500 | $10,500 | $10,512 | +$12 |
| 5 | $12,500 | $12,763 | $12,834 | +$334 |
| 10 | $15,000 | $16,289 | $16,470 | +$1,470 |
| 15 | $17,500 | $20,789 | $21,137 | +$3,637 |
| 20 | $20,000 | $26,533 | $27,126 | +$7,126 |
| 25 | $22,500 | $33,864 | $34,788 | +$12,288 |
| 30 | $25,000 | $43,219 | $44,677 | +$19,677 |
How Compounding Frequency Affects Growth
The more frequently interest compounds, the greater the final amount. For $10,000 at 5% for 30 years:
Annual compounding: A = 10000 × (1.05)^30 = $43,219.
Monthly compounding: A = 10000 × (1 + 0.05/12)^360 = $44,677.
Daily compounding: A = 10000 × (1 + 0.05/365)^10950 = $44,815.
Continuous compounding: A = 10000 × e^(0.05×30) = $44,817.
The difference between monthly and daily is small ($138). The big jump comes from annual to monthly (+$1,458). Beyond daily compounding, gains are negligible. Effective Annual Rate (EAR) = (1 + r/n)^n − 1 captures the true annual yield regardless of compounding frequency.
Rule of 72 — How Long to Double Your Money
The Rule of 72 is a quick estimate for compound interest doubling time: Years to double ≈ 72 / Interest Rate (%). At 6%: 72/6 = 12 years. At 9%: 72/9 = 8 years. At 2%: 72/2 = 36 years.
The rule works because ln(2) ≈ 0.693 and for small rates, (1+r)^t ≈ e^(rt). Solving e^(rt) = 2 gives t = ln(2)/r ≈ 0.693/r. Multiplying by 100/r gives 69.3/r (in years at r%). Using 72 instead of 69.3 gives a slightly conservative but more memorisable estimate.
Simple interest doubling time: Exactly 1/r years. At 5%: 20 years. At 6%: 16.67 years. At 9%: 11.11 years. Compare to compound interest Rule of 72: at 9%, 72/9 = 8 years. Compound interest doubles faster because of the interest-on-interest effect.
Real-World Applications
Savings account (compound): High-yield savings account at 4.5% APY (compounded daily). $10,000 over 5 years: A = 10000 × e^(0.045×5) ≈ $12,523. The "APY" (Annual Percentage Yield) already accounts for compounding frequency, making it easy to compare accounts.
Credit card debt (compound — enemy): Credit cards compound daily at 20%+ APR. Carrying $5,000 balance for 3 years at 22%: A = 5000 × (1 + 0.22/365)^1095 ≈ $9,563. You'd owe nearly double if you made no payments. Minimum payments largely cover interest, extending debt exponentially.
Mortgage (compound — long term): A $300,000 mortgage at 7% for 30 years (monthly compounding). Monthly payment ≈ $1,996. Total paid ≈ $718,560. Total interest paid = $418,560 — more than the original loan. This is compound interest working against the borrower over 30 years.
Investment portfolio (compound — friend): Investing $500/month at 8% annual return for 30 years. Final value ≈ $679,000 (over $500K in compound growth on just $180K contributed). This is the power of compound interest working for the investor.
Verdict
Simple interest grows linearly and is simpler to calculate; compound interest grows exponentially and generates dramatically more wealth (or debt) over long periods. For investors: compound is better. For borrowers: simple is better.
- ✓Use simple interest for: short-term calculations, T-bills, some personal loans, understanding basic interest concepts.
- ✓Use compound interest for: long-term investments, retirement accounts, mortgages, savings accounts — anything spanning years or decades.
- ✓The longer the time period and higher the rate, the bigger the gap between simple and compound interest.
- ✓Compounding frequency matters: monthly compounding yields noticeably more than annual at the same stated rate.
- ✓The Rule of 72 provides a quick mental estimate: years to double ≈ 72 / interest rate (%). Works only for compound interest.