**Date:** Wednesday, 28 October 2026 | **Time:** 4:00 PM IST **Category:** TNPSC Grp IV | **Section:** Aptitude & Mental Ability **Topic:** Simple Interest | **Progress:** Day 16/90
## 1. What is Simple Interest?
**Simple interest** is interest calculated only on the **original principal** (the amount borrowed or invested). The principal used for the calculation does not increase from one year to the next. At a fixed annual rate, the interest earned each year is the same.
**Principal (P):** Original amount borrowed or invested. **Interest (I):** Extra money paid or received for using the principal. **Rate (R):** Annual interest rate expressed as a percentage. **Time (T):** Duration expressed in years. **Amount (A):** Total of principal and interest.
Example: At 10% simple interest per annum on ₹1,000, the interest is ₹100 each year. For three years, the total interest is ₹300, because the calculation always uses the original ₹1,000.
## 2. Essential Formulas
1. **Simple Interest: I = (P × R × T) / 100** 2. **Total Amount: A = P + I** 3. **Principal: P = (100 × I) / (R × T)** 4. **Annual Rate: R = (100 × I) / (P × T)** 5. **Time in years: T = (100 × I) / (P × R)** 6. **Principal from amount: P = A / (1 + RT/100)**
**Converting time:** Six months = 6/12 = 0.5 year; eighteen months = 18/12 = 1.5 years. When the rate is per annum, time must be expressed in years.
## 3. Six Fully Worked Examples
### Example SI01 — Find Interest and Total Amount
**Question:** Find the simple interest and total amount on ₹12,000 at 8% per annum for 3 years.
**Solution:** P = 12,000; R = 8; T = 3. I = (12,000 × 8 × 3) / 100 = ₹2,880. A = P + I = 12,000 + 2,880 = ₹14,880. **Answer: Interest ₹2,880; total amount ₹14,880.**
### Example SI02 — Convert Months into Years
**Question:** Find the simple interest and amount on ₹8,000 at 7.5% per annum for 18 months.
**Solution:** T = 18/12 = 1.5 years. I = (8,000 × 7.5 × 1.5) / 100 = ₹900. A = 8,000 + 900 = ₹8,900. **Answer: Interest ₹900; total amount ₹8,900.**
### Example SI03 — Find the Principal
**Question:** A sum earns ₹2,400 as simple interest in 5 years at 8% per annum. Find the principal.
**Solution:** I = 2,400; R = 8; T = 5. P = (100 × 2,400) / (8 × 5) = 240,000 / 40 = ₹6,000. **Answer: Principal ₹6,000.**
### Example SI04 — Find the Annual Interest Rate
**Question:** A principal of ₹15,000 earns ₹2,700 simple interest in 3 years. Find the annual rate.
**Solution:** P = 15,000; T = 3; I = 2,700. R = (100 × 2,700) / (15,000 × 3) = 270,000 / 45,000 = 6. **Answer: 6% per annum.**
### Example SI05 — Find the Time
**Question:** How long does ₹20,000 take to become ₹24,800 at 6% simple interest per annum?
**Solution:** A = 24,800; P = 20,000; I = A − P = ₹4,800. T = (100 × 4,800) / (20,000 × 6) = 480,000 / 120,000 = 4. **Answer: 4 years.**
### Example SI06 — Compare Two Interest Rates
**Question:** On ₹10,000 for 2 years, what is the difference in simple interest between annual rates of 9% and 6%?
**Solution:** Difference in rates = 9 − 6 = 3 percentage points. Difference in interest = (10,000 × 3 × 2) / 100 = ₹600. Check: Interest at 9% = ₹1,800; at 6% = ₹1,200; difference = ₹600. **Answer: ₹600.**
## 4. Examination Shortcuts
**One-year interest:** P × R / 100. Example: ₹5,000 at 8% gives ₹400 per year, so four years gives ₹1,600.
**Doubling time:** For the same principal and fixed rate, doubling the time doubles simple interest.
**Comparing rates:** Difference in interest = P × (R₁ − R₂) × T / 100.
**Quick check:** With a positive rate, the total amount must exceed the principal. Always show the units: rupees, percent per annum, and years.
## 5. Common Mistakes
- Do not treat 18 months as 18 years. Convert it to 1.5 years. - Total amount (A) is not the same as interest (I). Interest = Amount − Principal. - Simple interest is always calculated on the original principal. **Compound interest** adds interest to the principal at specified intervals; that is a separate topic. - Do not use an annual rate as though it were a monthly rate. - These are mathematical examination examples, not statements of actual bank deposit or loan rates.
## 6. Textbook References and Book-Back Progress
**Primary mapping:** Tamil Nadu Samacheer Kalvi Class 7 Mathematics, Term 3, Chapter 2, *Percentage and Simple Interest*. A secondary exercise reproduction maps simple-interest problems to Exercise 2.4. The original government textbook and complete 2026–27 exercise inventory have not been checked directly.
**Supporting mapping:** Class 8 Mathematics, *Life Mathematics*, includes comparisons of simple and compound interest. Chapter and exercise numbering can differ between editions.
**Progress today:** Six original model worked examples; **0** authenticated textbook book-back questions; **0** Group IV PYQs checked against an official final answer key. **Complete current-edition book-back count: source not yet verified.**
**Pending:** Check every parent question and subquestion in Class 7 Term 3 Chapter 2 Exercise 2.4 against the original government textbook, then schedule complete verified batches in evening practice. Do not present secondary reproductions as verified official textbook questions.
## 7. Spaced Revision
**For today's Simple Interest topic:** +1 day 29 October; +3 days 31 October; +7 days 4 November; +14 days 11 November 2026. **Due today:** Day 15 Time and Work (+1), plus earlier planned +3/+7/+14 reviews. Continue the sequence without restarting earlier lessons.
## 8. ETN Push Notification
**Title:** 💰 TNPSC Group IV | Day 16 – Simple Interest! **Message:** Master principal, interest, rate and time through six fully solved examples. Today's complete bilingual Aptitude lesson is ready for ETN News.