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%\displaystyle 40\% is

Options

A7\displaystyle 7 years
B10\displaystyle 10 years
C17\displaystyle 17 years (apx.)
DNone of these
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Correct Answer

Option c17\displaystyle 17 years (apx.)

All Options:

  • A7\displaystyle 7 years
  • B10\displaystyle 10 years
  • C17\displaystyle 17 years (apx.)
  • DNone of these

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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)0.3364720.01980317 yearst = \frac{\ln(1.40)}{\ln(1.02)} \approx \frac{0.336472}{0.019803} \approx 17 \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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