**Simple interest formula**: **I = P × R × T**, where I = Interest, P = Principal (initial amount), R = Annual interest rate (decimal), T = Time (years). **Example**: $10,000 principal at 5% annual rate for 3 years. **Step 1**: Convert rate to decimal: 5% = 0.05. **Step 2**: I = $10,000 × 0.05 × 3 = **$1,500** total interest. **Step 3**: Final amount = $10,000 + $1,500 = **$11,500**. **Key characteristic**: Interest is calculated only on the original principal, NOT on accumulated interest (unlike compound interest). **Annual breakdown**: Year 1: $500 interest, Year 2: $500, Year 3: $500 (same each year). **Monthly interest**: $1,500 ÷ 36 months = $41.67/month. **Daily interest (Actual/365 method)**: ($10,000 × 0.05) ÷ 365 = $1.37/day. **Applications**: (1) Simple interest savings accounts (rare, most use compound). (2) Short-term loans <1 year (car title loans, payday loans). (3) Promissory notes and bonds (some use simple interest for coupon payments). (4) Interest-only loans during draw period. **Tax treatment**: Interest earned is taxable as ordinary income in year received (IRS Form 1099-INT for $10+ from banks).

**Calculation**: I = P × R × T = $5,000 × 0.04 × 2 = **$400** total interest. **Final amount**: $5,000 + $400 = **$5,400**. **Annual breakdown**: Year 1: $200 interest ($5,000 × 0.04 × 1), balance $5,200.

Year 2: $200 interest (still calculated on original $5,000 principal), final $5,400. **Monthly interest**: $400 ÷ 24 months = $16.67/month average. **Effective annual rate**: 4.00% (same as stated rate for simple interest). **Comparison to compound interest (annual compounding)**: Year 1: $200 interest, balance $5,200.

Year 2: $208 interest ($5,200 × 0.04), final **$5,408**. **Difference**: Compound earns $8 more ($408 vs $400) = 2% higher return. **When simple interest is used**: (1) Short-term CDs <1 year. (2) Bonds paying semi-annual coupons (interest not reinvested automatically). (3) Interest-only mortgage during initial 5-10 year period. (4) Personal loans with "add-on interest" (interest calculated upfront). **Real-world example**: 6-month CD at 4% simple interest: $5,000 × 0.04 × 0.5 = $100 interest.

Same CD with daily compounding: $101.01 = $1.01 more (0.5% difference).

**Simple interest**: Calculated only on original principal.

Formula: I = P × R × T.

Interest stays constant each period. **Compound interest**: Calculated on principal + accumulated interest.

Formula: A = P(1 + r/n)^(nt).

Interest grows each period. **Example comparison** ($10,000 at 5% for 10 years): **Simple interest**: Interest = $10,000 × 0.05 × 10 = **$5,000**.

Final amount: **$15,000**.

Annual interest: $500 every year (never changes). **Compound interest (annual)**: Year 1: $500, Year 2: $525, Year 3: $551.25..

Year 10 total: **$6,288.95**.

Final amount: **$16,288.95**. **Difference**: Compound earns **$1,288.95 more** (25.8% higher return). **Breakeven point**: Simple vs compound are equal at exactly 1 year ($500 both).

After 1 year, compound always wins. **Real-world usage**: **Simple interest used for**: (1) Short-term loans <1 year (payday loans, car title loans). (2) Interest-only mortgages (pay interest monthly, principal unchanged). (3) Bonds with semi-annual coupons (if not reinvested). (4) Some savings accounts (rare). **Compound interest used for**: (1) Most savings accounts (daily/monthly compounding). (2) CDs >1 year. (3) Mortgages (monthly compounding). (4) Credit cards (daily compounding). (5) Retirement accounts (401k, IRA). **Rule of 72**: Doubling time = 72 ÷ interest rate.

At 6%: Simple takes 16.67 years to double.

Compound takes 12 years (72 ÷ 6). **Key takeaway**: For savers: Demand compound interest.

For borrowers: Prefer simple interest (less total cost).

**Formula**: I = P × R × (Days ÷ Days_in_Year). **Two day-count methods**: **Actual/365 (Exact Days)**: Use actual number of days in period ÷ 365 (or 366 for leap years). **Example**: $10,000 at 6% for 90 days.

I = $10,000 × 0.06 × (90 ÷ 365) = **$147.95**. **30/360 (Banker's Rule)**: Assume 30 days/month, 360 days/year (simplifies calculations).

I = $10,000 × 0.06 × (90 ÷ 360) = **$150.00**. **Difference**: 30/360 method adds $2.05 (1.4% more interest) → Favors lender. **Calculating exact days** (Actual/365 method): **Step 1**: Count exact days between dates (e.g., Jan 15 - Apr 15 = 90 days).

Include start or end day, not both. **Step 2**: Check for leap year (Feb 29 exists → use 366, otherwise 365). **Step 3**: I = Principal × Rate × (Days ÷ 365 or 366). **Real-world applications**: **Actual/365**: (1) US Treasury bills. (2) Money market accounts. (3) Student loans (Stafford loans). (4) Most consumer loans. **30/360**: (1) Corporate bonds. (2) Municipal bonds. (3) Mortgage interest (some lenders). (4) Commercial loans. **Example comparison** ($50,000 at 8% for 45 days): Actual/365: $50,000 × 0.08 × (45 ÷ 365) = **$493.15**. 30/360: $50,000 × 0.08 × (45 ÷ 360) = **$500.00**.

Difference: $6.85 (30/360 costs 1.4% more). **Tax year consideration**: Interest accrued Dec 15, 2024 - Jan 15, 2025 (31 days) may be split across 2 tax years (16 days 2024, 15 days 2025) for IRS reporting.

**Common simple interest loans**: **1.

Auto loans (most common)**: Simple interest calculated daily on remaining principal balance. **Example**: $20,000 at 6% APR.

Daily interest rate: 0.06 ÷ 365 = 0.000164384.

Day 1 interest: $20,000 × 0.000164384 = $3.29.

If you pay early (Day 15 instead of Day 30), you save 15 days × $3.29 = $49.35. **Benefit**: Early/extra payments reduce principal immediately → Lower interest next period (unlike pre-computed interest). **2.

Student loans** (Federal Direct Loans, private loans): Simple interest accrues daily. **Forbearance/deferment**: Interest continues accruing. $30,000 loan at 5% = $4.11/day. 6-month forbearance = $750 unpaid interest capitalizes (adds to principal). **3.

Personal loans (some lenders)**: Advertised as "simple interest" but verify: True simple interest vs "add-on interest" (front-loaded). **Add-on scam**: $5,000 at 10% for 2 years.

Add-on calculates $1,000 interest upfront ($5,000 × 0.10 × 2).

Total owed: $6,000 ÷ 24 months = $250/month. **Actual APR**: ~18% (not 10%) because principal decreases each month but interest was calculated on full $5,000. **4.

Short-term loans** (<1 year): Payday loans, title loans, bridge loans. **Warning**: Rates often 15-30% for 2-4 weeks. $1,000 at 20% for 14 days: I = $1,000 × 0.20 × (14 ÷ 365) = $7.67. **APR equivalent**: (1 + $7.67/$1,000)^(365/14) - 1 = 21.9% annualized. **5.

Interest-only mortgages**: Pay interest monthly, no principal reduction during 5-10 year draw period. $300,000 at 6% interest-only = $1,500/month (stays constant).

After draw period: Principal + interest payments jump to $2,400/month (payment shock). **Loans that do NOT use simple interest**: (1) Credit cards (compound daily). (2) Most mortgages (amortized, not simple). (3) Pre-computed interest loans (Rule of 78s). **How to verify**: Ask lender "Is interest calculated daily on the current balance?" Yes = True simple interest.

**Truth**: Almost NO banks use simple interest for savings accounts anymore (switched to compound interest in 1980s-1990s for competitive advantage). **If a bank DID use simple interest** (hypothetical): **Daily simple interest method**: **Step 1**: Calculate daily interest rate: Annual rate ÷ 365.

Example: 3% ÷ 365 = 0.00008219. **Step 2**: Multiply by daily balance: $10,000 × 0.00008219 = $0.82/day. **Step 3**: Add interest at end of month: 30 days × $0.82 = $24.66 (even if balance grew to $10,500 mid-month, still calculated on $10,000 original). **Step 4**: Annual total: $10,000 × 0.03 × 1 = **$300** exactly. **Comparison to compound interest** (how real banks work): **Daily compounding (APY 3.045%)**: Day 1: $10,000 × (0.03 ÷ 365) = $0.82, balance $10,000.82.

Day 2: $10,000.82 × 0.00008219 = $0.82, balance $10,001.64. ..

Day 365: Final balance **$10,304.54**. **Difference**: Compound earns $4.54 more ($304.54 vs $300) = 1.5% higher return. **Why banks prefer compound**: (1) **Competitive**: "3.045% APY" sounds better than "3% simple interest." (2) **Customer retention**: Compound interest rewards customers for keeping money in account longer. (3) **Regulatory**: Truth in Savings Act (1991) requires APY disclosure (assumes compounding). **Where simple interest IS still used**: (1) **Money market funds** (some calculate daily simple interest, pay monthly). (2) **Short-term CDs** <6 months (some banks). (3) **Checking accounts** with interest (rare, most use compound). **How to check your bank statement**: Look for "APY" vs "Interest Rate." APY = (1 + r/n)^n - 1 (means compounding).

If APY equals interest rate exactly → Simple interest (extremely rare). **Example**: 5% interest rate with daily compounding = 5.127% APY.

If your statement shows APY = 5.000% → Simple interest (or no compounding).