ENGLISH VERSION — COMPLETE MATCHING LESSON
TNPSC Group IV: Compound Interest – Formulas, Shortcuts and 8 Fully Worked Examples
1. What Is Compound Interest?
Compound interest (CI) is interest calculated on the original principal and on interest added at the end of earlier compounding periods. It is often called interest on interest.
Simple interest (SI) is calculated only on the original principal. Compound interest adds interest to the principal after each compounding period.
Symbols: - P = Principal (original amount) - R = Annual interest rate (%) - T = Time in years - A = Amount (principal plus interest) - CI = Compound Interest - SI = Simple Interest
2. Essential Formulas
Compounded annually: A = P × (1 + R/100)^T CI = A − P
Simple interest for comparison: SI = P × R × T / 100
Compounded half-yearly: A = P × (1 + R/200)^(2T). Divide the annual rate by 2 and multiply the number of years by 2.
Compounded quarterly: A = P × (1 + R/400)^(4T). Divide the annual rate by 4 and multiply the number of years by 4.
Different rates in successive years: A = P × (1 + R₁/100) × (1 + R₂/100) × (1 + R₃/100) …
Depreciation (decrease in value): Remaining value = P × (1 − R/100)^T
Difference between CI and SI for exactly two years at the same annual rate, compounded annually: CI − SI = P × (R/100)^2
Find the original principal: P = A / (1 + R/100)^T
Important qualification: For textbook problems specifying annual compounding over a non-whole number of years, interest for complete years may be compounded, with simple interest used for the remaining fraction of a year. Always follow the compounding convention stated in the question.
3. Understand the Idea in One Minute
Suppose the principal is ₹1,000 and the annual compound interest rate is 10%.
- Year 1 interest = ₹100; new amount = ₹1,100. - Year 2 interest = ₹110; new amount = ₹1,210. - Total compound interest after two years = ₹210. - Simple interest for the same period = ₹200.
The extra ₹10 comes from earning interest on the first year’s interest.
4. Eight Fully Worked Original Model Examples
Example 1 – Annual compounding Question: Find the CI on ₹12,000 at 10% per annum for two years. Solution: P=12,000; R=10; T=2. A = 12,000 × (1.10)^2 = 12,000 × 1.21 = ₹14,520. CI = 14,520 − 12,000 = ₹2,520.
Example 2 – Half-yearly compounding Question: Find the CI on ₹6,000 at 12% per annum for one year, compounded every six months. Solution: Rate per half-year = 12/2 = 6%; number of periods = 2. A = 6,000 × (1.06)^2 = 6,000 × 1.1236 = ₹6,741.60. CI = 6,741.60 − 6,000 = ₹741.60.
Example 3 – CI minus SI shortcut Question: Find CI − SI on ₹7,500 at 8% per annum for two years, compounded annually. Solution: CI − SI = P × (R/100)^2. = 7,500 × (0.08)^2 = 7,500 × 0.0064 = ₹48. Check: SI = ₹1,200; CI = ₹1,248; difference = ₹48.
Example 4 – Two and a half years Question: ₹8,000 earns 10% per annum for 2½ years, compounded annually for complete years and earning simple interest for the remaining half-year. Find CI. Solution: After two full years, A₂ = 8,000 × (1.1)^2 = ₹9,680. Interest for the next half-year = 9,680 × 10 × 0.5 / 100 = ₹484. Final amount = 9,680 + 484 = ₹10,164. CI = 10,164 − 8,000 = ₹2,164.
Example 5 – Changing annual rates Question: Find the CI on ₹10,000 if the annual rates for three consecutive years are 10%, 15%, and 20%. Solution: A = 10,000 × 1.10 × 1.15 × 1.20. = 10,000 × 1.518 = ₹15,180. CI = 15,180 − 10,000 = ₹5,180.
Example 6 – Depreciation Question: A machine worth ₹24,000 loses 25% of its value every year. What is its value after two years? Solution: Remaining value = 24,000 × (1 − 25/100)^2. = 24,000 × (0.75)^2 = 24,000 × 0.5625 = ₹13,500. Total depreciation = ₹10,500.
Example 7 – Finding principal Question: An amount becomes ₹11,025 in two years at 5% compound interest per annum. Find the original principal. Solution: P = 11,025 / (1.05)^2. = 11,025 / 1.1025 = ₹10,000.
Example 8 – Quarterly compounding Question: Find CI on ₹8,000 at 8% per annum for nine months, compounded quarterly. Solution: Quarterly rate = 8/4 = 2%; nine months contain three quarters. A = 8,000 × (1.02)^3 = 8,000 × 1.061208 = ₹8,489.664. CI = 8,489.664 − 8,000 = ₹489.664 ≈ ₹489.66, rounded to two decimal places.
All eight worked examples are original model problems for teaching. None is represented as a verified TNPSC previous-year question or authenticated book-back question.
5. Fast Exam Shortcuts
1. For CI − SI over two full years: use P × (R/100)^2 rather than calculating both amounts separately. 2. At 10% per year: multiply the amount by 1.1 each year. 3. At 20% per year: multiply the amount by 1.2 each year. 4. Half-yearly compounding: halve the annual rate and double the number of periods. 5. Depreciation: use (1 − R/100), not (1 + R/100). 6. Money answers: round to two decimal places only where appropriate; retain precision during intermediate steps.
6. Common Mistakes
Mistake: Writing CI = P × R × T / 100. That is the simple-interest formula. Correct: CI = P(1 + R/100)^T − P.
Mistake: Using the full annual rate in every six-month period. Correct: Half-yearly rate is R/2; number of periods is 2T.
Mistake: Adding the depreciation percentage to the value. Correct: Reduce the remaining value at the end of each year.
Mistake: Automatically raising to the power 2.5 in every 2½-year problem. Correct: Read the stated compounding interval and treatment of the extra half-year.
7. Textbook and Complete Book-Back Progress
Official TNPSC syllabus: Aptitude and Mental Ability, SSLC standard, Compound Interest. Related textbook: Tamil Nadu Samacheer Kalvi Class 8 Mathematics, Chapter 4 – Life Mathematics, Compound Interest. Exercise provisionally identified by two secondary solution guides: Exercise 4.3. However, the original 2026–27 government textbook and full exercise inventory are source not yet verified.
Provisional inventory: A secondary guide indexes Q1(i)–1(v), Q2(i)–2(v), and Q3–Q15: 23 individual question parts. This is not a verified complete original-textbook count.
Proposed additional evening practice batches: - Batch 1/4: Q1(i)–1(v), 5 parts. - Batch 2/4: Q2(i)–2(v), 5 parts. - Batch 3/4: Q3–Q9, 7 questions. - Batch 4/4: Q10–Q15, 6 questions.
Authenticated book-back questions completed today: 0/23 provisionally indexed. Awaiting original-source verification: 23 provisional parts, plus any additional items not captured by the guide. Verified TNPSC PYQs included today: 0.
Online sources disagree about the topic assigned to Class 8 Mathematics Exercise 4.4 in the previous Time and Work lesson. That earlier exercise reference should be rechecked against the original textbook before treating its coverage as complete.
8. Spaced Revision
Revise today’s Compound Interest topic on 25 October (+1), 27 October (+3), 31 October (+7), and 7 November (+14), 2026. Today also briefly revise yesterday’s Time and Work lesson (+1). The 7 PM practice will contain two headline questions on today’s Compound Interest topic.
9. ETN Push Notification – English
Title: 🔢 TNPSC Group IV | Day 12 – Compound Interest! Message: 📚 Learn annual, half-yearly and quarterly compound interest, CI–SI differences, and depreciation with 8 fully worked examples in today’s 4 PM Aptitude lesson on ETN News.
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Sources and verification / ஆதாரங்கள்
1. Official TNPSC Group IV syllabus (English) — Compound Interest is included under Part B, Aptitude and Mental Ability, Unit I. https://tnpsc.gov.in/static_pdf/syllabus/final_g4_syll_english.pdf 2. Official TNPSC revised examination scheme — 100 Tamil, 75 General Studies, 25 Aptitude/Reasoning questions. https://tnpsc.gov.in/static_pdf/syllabus/G4_Scheme_Revised_27012022.pdf 3. Secondary Class 8 Mathematics Exercise 4.3 guide (not the original government textbook): https://samacheerkalvi.guide/samacheer-kalvi-8th-maths-guide-chapter-4-ex-4-3/ 4. Independent secondary Exercise 4.3 reference (not the original government textbook): https://www.saranextgen.com/help/2Bm/2Mt/exercise-4-3-chapter-4-life-mathematics-8th-maths-guide-samacheer-kalvi-solutions-tamil-medium
Source integrity: Secondary solution pages contain some typographical and formula errors; numerical solutions above were calculated independently. Exercise mapping is provisional until checked against the original government textbook. No scanned answer tick is treated as an official TNPSC final key. No publication or push notification has been performed.
Next session / அடுத்த பயிற்சி: 24 October 2026, 7:00 PM — exactly 15 headline MCQs: 8 General Tamil (வேர்ச்சொல் மற்றும் வினை வடிவங்கள்), 5 General Studies (உள்ளாட்சி அமைப்புகள்), 2 Aptitude (கூட்டு வட்டி), plus separately tracked additional book-back practice only where source verification permits.
