Mathematics of FinanceMCQPYQ Jan 21Question 1214 of 512
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The population of a town increase by 2%\displaystyle 2\% of the population at the beginning of the year. The number of year by which the total increases in population would be 40%\displaystyle 40\% is:

Options

A7\displaystyle 7 years
B10\displaystyle 10 years
C17\displaystyle 17 years
D19\displaystyle 19 years (approx.)
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Correct Answer

Option c17\displaystyle 17 years

All Options:

  • A7\displaystyle 7 years
  • B10\displaystyle 10 years
  • C17\displaystyle 17 years
  • D19\displaystyle 19 years (approx.)

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Detailed Solution & Explanation

**Derivation of Time for Population to Increase by 40%** Given: - Present Population = P0\displaystyle P_0 - Annual growth rate (r\displaystyle r) = 2%\displaystyle 2\% per annum - Target Increase = 40%\displaystyle 40\%, meaning final population Pn=1.40P0\displaystyle P_n = 1.40 P_0. **Step 1: Set up the geometric growth equation** Pn=P0(1+r)nP_n = P_0(1 + r)^n 1.40P0=P0(1+0.02)n1.40 P_0 = P_0(1 + 0.02)^n 1.40=(1.02)n1.40 = (1.02)^n **Step 2: Solve for n\displaystyle n using logarithms** ln(1.40)=nln(1.02)\ln(1.40) = n \ln(1.02) n=ln(1.40)ln(1.02)n = \frac{\ln(1.40)}{\ln(1.02)} Using log values: ln(1.40)0.336472\ln(1.40) \approx 0.336472 ln(1.02)0.019803\ln(1.02) \approx 0.019803 n=0.3364720.01980316.99 years17 yearsn = \frac{0.336472}{0.019803} \approx 16.99 \text{ years} \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.

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