Growth & Depreciation Applications

Population बढ़ना, कीमत घटना

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Growth & Depreciation Applications

  • Compound Interest
  • Growth & Depreciation Applications
नमस्ते दोस्तों! MeraExam में आपका स्वागत है। आज की class में समझेंगे — Population बढ़ना, कीमत घटना। बिलकुल zero से, एकदम आसान भाषा में। चलिए शुरू करते हैं!
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Learning Objective

Apply compound formulas to population growth, depreciation and back-dated values.

🎯 Learning Objective

Apply compound formulas to population growth, depreciation and back-dated values.

💡 Concept

  • Growth (population, price, bacteria): Future = P(1 + r/100)ⁿ
  • Depreciation (machine, vehicle value): Future = P(1 − r/100)ⁿ
  • Value n years AGO: divide — Past = P/(1 + r/100)ⁿ
  • Different rates in different years → multiply the factors one by one
  • Increase and decrease in successive years mix signs: ×1.1 then ×0.95

🧮 Key Formulas

Growth: P(1 + r/100)ⁿ

>

Depreciation: P(1 − r/100)ⁿ

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n years ago: P ÷ (1 + r/100)ⁿ

✏️ Easy Example

Q. The population of a town is 20,000 and grows at 10% per year. Find the population after 2 years.

  1. 20000 × 1.1 = 22000
  2. 22000 × 1.1 = 24200

Answer: 24,200

🇮🇳 Real-Life Example

A ₹80,000 bike loses 15% value every year — after one year the resale apps quote around ₹68,000. That is depreciation compounding against you.

📝 Exam-Level Example

Q. A machine worth ₹50,000 depreciates at 20% per annum. Find its value after 2 years.

  1. 50000 × 0.8 = 40000
  2. 40000 × 0.8 = 32000

Answer: ₹32,000

📝 Exam-Level Example

Q. A town's population rose 10% in the first year and fell 5% in the second year. If it is now 20,900, find the population 2 years ago.

  1. P × 1.10 × 0.95 = 20900
  2. P × 1.045 = 20900
  3. P = 20900 ÷ 1.045

Answer: 20,000

🪄 Memory Trick

Draw the timeline and hang the factor on each year: up 10% → ×1.1, down 5% → ×0.95. Past value → divide by the whole chain.

⚠️ Common Mistakes

  • ❌ Using simple growth (P + n × r% of P) instead of compound
  • ❌ Multiplying by (1 + r/100)ⁿ when the question asks for a PAST value
  • ❌ Using 1 + r/100 for depreciation instead of 1 − r/100

🏆 Exam Tips

  • ✅ Population, bacteria, price rise → plus sign; machine, vehicle, mobile value → minus sign
  • ✅ Mixed-rate years cannot use the power formula — chain the factors instead

📌 Summary

  • Growth = P(1 + r/100)ⁿ, depreciation = P(1 − r/100)ⁿ
  • Back in time → divide, not multiply
  • Different yearly rates → multiply factors one by one
  • Population maths = CI maths in disguise
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