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The Formula
Simple Interest (I) = Principal (P) × Rate (R) × Time (T)
Where:
- Principal: The original amount borrowed or invested
- Rate: The annual interest rate (as a decimal)
- Time: The number of years
Example
$10,000 loan at 5% annual simple interest for 3 years:
I = $10,000 × 0.05 × 3 = $1,500
Total amount owed: $10,000 + $1,500 = $11,500
Annual Breakdown
Year 1:
- Interest: $10,000 × 0.05 = $500
- Balance: $10,500
Year 2:
- Interest: $10,000 × 0.05 = $500 (only on original principal)
- Balance: $11,000
Year 3:
- Interest: $10,000 × 0.05 = $500
- Balance: $11,500
Key observation: Interest is identical each year ($500). It's not calculated on the growing balance (which would be compound interest).
Simple Interest vs. Compound Interest
Compound Interest Example (same loan):
Year 1:
- Interest: $10,000 × 0.05 = $500
- Balance: $10,500
Year 2:
- Interest: $10,500 × 0.05 = $525 (on the growing balance)
- Balance: $11,025
Year 3:
- Interest: $11,025 × 0.05 = $551.25
- Balance: $11,576.25
Comparison:
- Simple interest final balance: $11,500
- Compound interest final balance: $11,576.25
- Difference: $76.25
With compound interest, you pay more because interest is calculated on larger and larger balances.
Where Simple Interest Is Used
Bonds: A bond might pay 4% simple interest annually on the face value. A $1,000 bond at 4% pays $40/year regardless of how long you hold it.
Some loans: Short-term loans sometimes use simple interest. A 6-month car title loan might use simple interest calculations.
Short-term instruments: Treasury bills and short-term certificates of deposit sometimes use simple interest.
Why Most Lenders Prefer Compound Interest
Lenders much prefer compound interest because it generates more total interest:
$10,000 at 5% for 10 years:
- Simple interest: $10,000 + (10,000 × 0.05 × 10) = $15,000
- Compound interest: $10,000 × 1.05^10 = $16,288.95
- Difference: $1,288.95 more with compound interest
This is why most mortgages, credit cards, and savings accounts use compound interest—it benefits lenders (if you borrow) and savers (if you save).
Simple Interest in Investments
In investing contexts, simple interest is rare. Most investments (stocks, bonds, mutual funds) use compound interest because returns are reinvested.
But understanding simple interest is foundational. It's the building block for understanding compound interest, amortization, and loan calculations.
Simple Interest vs. APR
Many consumer loans state an APR (Annual Percentage Rate) but calculate interest using amortization (a blend of simple and compound interest).
Example: A mortgage lists 6% APR but uses amortization
- The 6% is roughly the simple interest rate annually
- But the actual calculation uses amortization (interest on remaining balance)
- So the actual cost is compound, not simple
This is why understanding the difference matters: APR is stated simply, but actual calculations are often more complex.
The Bottom Line
Simple interest is the foundation. It's interest only on principal. Most real-world lending uses compound interest (interest on interest), which costs more or earns more depending on whether you're borrowing or saving.
Understanding simple interest helps you understand the more complex compound interest calculations used in actual financial products.
