Simple interest is calculated only on the original principal — not on accumulated interest. The formula is I = PRT (Interest = Principal × Rate × Time). On a $10,000 auto loan at 6% simple interest for 4 years, total interest is $2,400, making the total repayment $12,400.
The Simple Interest Formula: I = PRT
$$I = P \times R \times T$$
Where:
- I = interest earned or owed
- P = principal (starting amount)
- R = annual interest rate (as a decimal; 6% = 0.06)
- T = time in years
To find the total amount at the end of the period:
$$A = P + I = P(1 + RT)$$
Worked Examples
Example 1: Auto Loan
You borrow $18,000 for a car at 5.5% simple interest over 5 years.
$$I = 18{,}000 \times 0.055 \times 5 = $4{,}950$$ $$A = 18{,}000 + 4{,}950 = $22{,}950 \text{ total repaid}$$
Monthly payment ≈ $22,950 ÷ 60 months = $382.50/month
Example 2: Savings Bond (T-Bill)
You invest $5,000 in a 6-month Treasury bill yielding 5.25% annually.
T = 0.5 years (6 months)
$$I = 5{,}000 \times 0.0525 \times 0.5 = $131.25$$
You receive $5,131.25 at maturity.
Example 3: Personal Loan
You borrow $3,000 at 8% simple interest for 18 months (T = 1.5 years):
$$I = 3{,}000 \times 0.08 \times 1.5 = $360$$ $$A = $3{,}360 \text{ total repaid}$$
Simple Interest vs. Compound Interest
The key difference: simple interest is linear; compound interest is exponential.
| Scenario | Simple Interest | Compound (Monthly) | Difference |
|---|---|---|---|
| $10,000 at 5% for 1 year | $500 | $511.62 | $11.62 |
| $10,000 at 5% for 5 years | $2,500 | $2,833.59 | $333.59 |
| $10,000 at 5% for 10 years | $5,000 | $6,470.09 | $1,470.09 |
| $10,000 at 5% for 20 years | $10,000 | $17,121.75 | $7,121.75 |
The longer the term, the more compound interest outpaces simple interest. For savings accounts, you almost always want compound interest — and the higher the APY, the better.
Quick Reference: Simple Interest Table
For a $10,000 principal at various rates over 1 year:
| Rate | Interest (1 yr) | Rate | Interest (1 yr) |
|---|---|---|---|
| 1% | $100 | 6% | $600 |
| 2% | $200 | 7% | $700 |
| 3% | $300 | 8% | $800 |
| 4% | $400 | 9% | $900 |
| 5% | $500 | 10% | $1,000 |
Which Products Use Simple Interest?
| Product | Interest Type |
|---|---|
| Most auto loans | Simple |
| US Treasury bills (T-bills) | Simple (discount basis) |
| Some personal loans | Simple |
| Certificate of deposit (CDs) | Often simple for short terms |
| Most savings accounts | Compound (daily) |
| Credit cards | Compound (daily) — much more expensive |
| Most mortgages | Amortized (effectively simple on declining principal) |
Rearranging the Formula
You can solve for any variable if you know the other three:
| To Find | Formula |
|---|---|
| Interest (I) | I = P × R × T |
| Principal (P) | P = I ÷ (R × T) |
| Rate (R) | R = I ÷ (P × T) |
| Time (T) | T = I ÷ (P × R) |
Example: How long to earn $750 in simple interest on $5,000 at 5%?
$$T = 750 \div (5{,}000 \times 0.05) = 750 \div 250 = 3 \text{ years}$$
For a deeper dive into how interest compounds over time and grows wealth, see What Is Compound Interest. For current deposit rates that use compounding, visit the Interest Rates & Federal Reserve hub.
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