**Day 06 | Sunday, 18 October 2026 | 4:00 PM IST** **Category: TNPSC Grp IV | Aptitude & Mental Ability – Simple Interest**
### 1. What is simple interest?
**Simple interest** is interest calculated on the original amount of money borrowed or invested. The original amount stays the same for the interest calculation every year; interest is not added to the principal for calculating the next year's interest. For example, at 10% simple interest per year on ₹10,000, the interest is ₹1,000 every year: ₹2,000 for two years and ₹3,000 for three years.
**Key terms:** Principal (P) – original money; Interest (I) – extra money paid or earned; Rate (R) – percentage per year; Time (T) – duration in years; Amount (A) – principal plus interest.
### 2. Essential formulas
**Simple Interest: I = (P × R × T) / 100** **Amount: A = P + I** **Principal: P = (100 × I) / (R × T)** **Rate: R = (100 × I) / (P × T)** **Time: T = (100 × I) / (P × R)** **Principal from amount: P = 100A / (100 + RT)**
These formulas assume **R is an annual percentage rate** and **T is measured in years**. Convert months into years: T = number of months/12. Six months = 1/2 year; nine months = 3/4 year; one year and eight months = 1 + 8/12 = 5/3 years.
### 3. Seven fully worked examples
**Example 1 – Find interest and amount:** Calculate simple interest and the total amount on ₹12,500 at 8% per year for 3 years.
P = 12,500; R = 8; T = 3. I = (12,500 × 8 × 3)/100 = **₹3,000**. A = 12,500 + 3,000 = **₹15,500**. **Answer: Interest ₹3,000; total amount ₹15,500.**
**Example 2 – Convert months into years:** Find the simple interest on ₹18,000 at 7.5% per year for 1 year and 8 months.
T = 1 + 8/12 = 5/3 years. I = (18,000 × 7.5 × 5/3)/100 = 180 × 12.5 = **₹2,250**. A = 18,000 + 2,250 = **₹20,250**. **Answer: Interest ₹2,250; total amount ₹20,250.**
**Example 3 – Find the interest rate:** A principal of ₹24,000 earns ₹4,320 simple interest in 3 years. What is the annual rate?
R = (100 × 4,320)/(24,000 × 3) = 432,000/72,000 = **6%**. **Answer: 6% per year.**
**Example 4 – Find the time:** How many years will ₹12,000 take to become ₹14,700 at 7.5% simple interest per year?
I = A − P = 14,700 − 12,000 = ₹2,700. T = (100 × 2,700)/(12,000 × 7.5) = 270,000/90,000 = **3 years**. **Answer: 3 years.**
**Example 5 – Find the principal:** Simple interest is ₹2,700 at 9% per year for 2.5 years. Find the principal.
P = (100 × 2,700)/(9 × 2.5) = 270,000/22.5 = **₹12,000**. **Answer: ₹12,000.**
**Example 6 – Money doubles:** A sum doubles in 8 years under simple interest. Find the annual interest rate.
Doubling means A = 2P, so I = A − P = P. P = (P × R × 8)/100. Cancel P from both sides: 1 = 8R/100. R = 100/8 = **12.5%**. **Answer: 12.5% per year.**
**Example 7 – Find principal from the amount:** After 3 years at 10% annual simple interest, the total amount is ₹15,600. Find the original principal.
A = P(1 + RT/100) = P(1 + 10×3/100) = 1.3P. P = 15,600/1.3 = **₹12,000**. Check: Interest = 12,000 × 10 × 3/100 = ₹3,600; total = ₹15,600. **Answer: ₹12,000.**
### 4. Quick shortcuts for TNPSC
**One-year interest:** P × R/100. Multiply this by T years to get simple interest. **Doubling rule:** If a sum doubles in T years at simple interest, R = 100/T. **Tripling rule:** If a sum triples in T years, R = 200/T. **Direct proportion:** If principal and rate stay fixed, simple interest increases in direct proportion to time. **Interest versus amount:** If the question asks for *interest*, give I. If it asks for the *total amount*, give A = P + I. **Simple versus compound interest:** Simple interest is always calculated on the original principal. Compound interest can also earn interest on earlier interest. Compound interest will be covered as a separate lesson.
### 5. Common mistakes and one-minute revision
Never use months directly as years. Eighteen months = 1.5 years; two years and three months = 2.25 years. When the rate is given per annum, convert time into years. At 5% per year on ₹10,000, one year's interest is ₹500, three years' simple interest is ₹1,500, and the final amount is ₹11,500.
**Memorise: I = PRT/100; A = P + I; R = 100I/PT; T = 100I/PR; P = 100I/RT.**
### 6. Textbook reference and book-back progress
**Primary reference:** Tamil Nadu Samacheer Kalvi, Class 7 Mathematics, Term 3, Chapter 2 – *Percentage and Simple Interest*. A third-party exercise guide identifies **Exercise 2.4** as covering simple interest. **The complete original 2026–27 government textbook exercise has not yet been independently verified (source not yet verified).** Its exact total number of questions cannot currently be confirmed.
**Today's seven problems:** All are *original instructional examples*, not verified textbook book-back questions or TNPSC previous-year questions. **Verified original book-back questions completed:** 0. **Remaining count:** To be determined after verifying the full original exercise. **7 PM practice:** Two Aptitude MCQs will test today's simple-interest lesson. Any separately verified book-back batch will be outside the 15 headline questions.
### 7. Spaced revision
**Day 06 simple-interest revision:** 19 October (+1), 21 October (+3), 25 October (+7), and 1 November (+14). Today also revise yesterday's HCF and LCM lesson as its one-day checkpoint. **Official syllabus:** The TNPSC Group IV SSLC Aptitude Unit I explicitly includes both simple and compound interest as separate topics.
### 8. ETN push notification – English
**Title:** 🔢 TNPSC Group IV | Simple Interest Made Easy! **Message:** 📚 Master interest, principal, time and rate with simple formulas and 7 fully worked examples. Read the complete Day 06 Aptitude lesson on ETN News!
