Mathematics of FinanceMCQPYQ May 19Question 1285 of 512
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The population of a town increases every year by 2%\displaystyle 2\% of the population beginning of that year. The number of years by which the total increase of population be $40\%$ is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $17$ years (apx.)

All Options:

  • A7\displaystyle 7 years
  • B$10$ years
  • C$17$ years (apx.)
  • DNone of these

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 = $40\%,meaning\displaystyle , meaningP_t = 1.40 P_0$ **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 = ln⁡(1.40)ln⁡(1.02)\displaystyle \frac{\ln(1.40)}{\ln(1.02)} ≈\displaystyle \approx 0.3364720.019803\displaystyle \frac{0.336472}{0.019803} ≈\displaystyle \approx 17  years\displaystyle \text{ years} Hence, **Option C** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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