Mathematics of FinanceMCQMTP Dec 23 Series IQuestion 1397 of 512
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The population of a town increases by 2%\displaystyle 2\% of the population at the beginning of the year. The number of years by which the total increases in population would be 40%\displaystyle 40\% is

Options

A7 years
B10 years
C17 years
D19 years
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Correct Answer

Option c17 years

All Options:

  • A7 years
  • B10 years
  • C17 years
  • D19 years

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Detailed Solution & Explanation

**Derivation of Required Period** Given: - Annual growth rate (r\displaystyle r) = 2%\displaystyle 2\% per annum - Target population increase = 40%\displaystyle 40\% (so Amount A=1.40P0\displaystyle A = 1.40 P_0) **Step 1: Set up the growth equation** A=P0(1+r)tA = P_0(1 + r)^t 1.40P0=P0(1+0.02)t1.40 P_0 = P_0(1 + 0.02)^t 1.40=(1.02)t1.40 = (1.02)^t **Step 2: Solve for t\displaystyle t using logarithms** ln(1.40)=tln(1.02)\ln(1.40) = t \ln(1.02) t=ln(1.40)ln(1.02)t = \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 t=0.3364720.01980316.99 years17 yearst = \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.

View Official ICAI Syllabus

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