Mathematics of FinanceMCQPYQ May 19 Series IIQuestion 1288 of 512
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The annual birth rate and death rate per $1000\displaystyle are $39.4 and $19.4$ respectively. The number of years in which population will be doubled assuming that there is no immigration or emigration approximately.

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

✅ Option c — $35$ years

All Options:

  • A$30$ years
  • B$30$ years
  • C$35$ years
  • D$25$ years

Detailed Solution & Explanation

**Derivation of Population Doubling Time** Given: - Birth rate = $39.4\displaystyle per $1,000 - Death rate = $19.4\displaystyle per $1,000 **Step 1: Calculate the net annual growth rate (r\displaystyle r)** Net Growth Rate per 1,000=39.4−19.4=20Net Growth Rate per 1,000=39\displaystyle \text{Net Growth Rate per 1,000} = 39.4 - 19.4 = 20 r=201000=2%=0.02 per annumr = 201000=2\displaystyle \frac{20}{1000} = 2\% = 0.02  per annum\displaystyle \text{ per annum} **Step 2: Set up the population doubling equation** (1+r)t=2(1 + r)^t = 2 (1.02)t=2(1.02)^t = 2 **Step 3: Solve for t\displaystyle t using logarithms** t=ln⁡(2)ln⁡(1.02)≈0.6931470.019803≈35 yearst = ln⁡(2)ln⁡(1.02)\displaystyle \frac{\ln(2)}{\ln(1.02)} ≈\displaystyle \approx 0.6931470.019803\displaystyle \frac{0.693147}{0.019803} ≈\displaystyle \approx 35  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.

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