Mathematics for FinancePYQ Jun 23Question 1247 of 512
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The population of a town increases every year by 2%\displaystyle 2\% of the population at the beginning of that year. The approximate number of years by which the total increase of population will be 40%\displaystyle 40\%, is (Given 1.02x=1.17166\displaystyle 1.02^x = 1.17166)

Options

A15
B17
C19
D20
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Correct Answer

✅ Option b — 17

All Options:

  • A15
  • B17
  • C19
  • D20

Detailed Solution & Explanation

**Derivation of Growth Period to Reach 40% Increase** Given: - Growth rate (r\displaystyle r) = 2%\displaystyle 2\% per annum - Target population increase = 40%\displaystyle 40\%, meaning Pt=1.40P0\displaystyle P_t = 1.40 P_0 **Step 1: Set up the growth equation** Pt=P0(1+r)tP_t = P_0(1 + r)^t 1.40P0=P0(1.02)t1.40 P_0 = P_0(1.02)^t 1.40=(1.02)t1.40 = (1.02)^t **Step 2: Solve for t\displaystyle t using logarithms** t=ln⁡(1.40)ln⁡(1.02)≈0.3364720.019803≈17 yearst = \frac{\ln(1.40)}{\ln(1.02)} \approx \frac{0.336472}{0.019803} \approx 17 \text{ years} Hence, **Option B** is the correct answer.

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