Question 32 of 45advanced🔍 AnalyzeShort Answer4 marks

Consider an amount ₹1000. If this grows at 10% p.a., how long will it take to double when compounding is done vs. when compounding is not done? Is compounding an example of exponential growth and not-compounding an example of linear growth?

Correct Answer

Without Compounding (Simple Interest): To double from ₹1000 to ₹2000, interest needed = ₹1000 Interest per year = ₹1000×0.101000 \times 0.10 = ₹100 Time = ₹1000 ÷ ₹100 = 10 years

With Compounding: Find t where: 1000 × (1.10)^t = 2000 (1.10)^t = 2 t ≈\approx 7.3 years

Conclusion: Yes, compounding is exponential growth (amount grows by multiplying). Simple interest is linear growth (amount grows by adding constant interest each period).

Exercise: Figure it Out (Section 4) | Q: 7 | (Page Page 24)
For More Understanding

Explanation

The chapter distinguishes between linear growth (simple interest) and exponential growth (compound interest). Exponential growth accelerates over time because each period's growth builds on the previous period's total.

Solution Steps

  1. Without compounding:

  2. Interest per year = 1000×0.101000 \times 0.10 = ₹100

  3. To double: need ₹1000 interest

  4. Time = 1000/100 = 10 years

  5. With compounding:

  6. 1000 × (1.10)^t = 2000

  7. (1.10)^t = 2

  8. t ≈\approx 7.3 years (using logarithms or trial)

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